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Explain the solution process for the given equation.
product of two natural numbers is 5 . then , the sum of reciprocals of their squares is a ) 290 / 289 , b ) 26 / 25 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
"explanation : if the numbers are a , b , then ab = 5 , as 17 is a prime number , so a = 1 , b = 5 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 5 ( 2 ) = 26 / 25 option b"
Break down and solve the equation step by step.
a = 5 ^ 15 - 125 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ? a ) none , b ) one , c ) two , d ) three , e ) four
"this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get none different values and answer is a . . . ."
Provide a detailed solution to the given mathematical problem.
find value for x from below equation ? x + 1 = 2 a ) - 5 , b ) 1 , c ) 4 , d ) 3 , e ) 2
"1 . subtract 1 from both sides : x + 1 - 1 = 2 - 1 2 . simplify both sides : x = 1 b"
Explain the solution process for the given equation.
a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 54 . find the number of notes of rs . 50 denomination . a ) 15 , b ) 21 , c ) 37 , d ) 19 , e ) 21
"total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 54 - x now , 50 * x + 500 * ( 54 - x ) = 10350 50 x + 27000 - 500 x = 10350 - 450 x = - 16650 x = 37 . no . of 50 rupees note = 37 . answer : option c"
Work through the equation methodically, ensuring clarity at each step.
a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 10 per sq m ? a ) 6350 , b ) 7357 , c ) 6328 , d ) 6750 , e ) 7560
"area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 10 = rs . 6750 answer : d"
Solve the problem systematically, showing each step clearly.
how many 3 digit number contain number 4 ? a ) 352 , b ) 268 , c ) 236 , d ) 252 , e ) 354
"total 3 digit no . = 9 * 10 * 10 = 900 not containing 4 = 8 * 9 * 9 = 648 total 3 digit number contain 4 = 900 - 648 = 252 answer : d"
Solve the problem systematically, showing each step clearly.
how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 140 m in length ? a ) 16.5 , b ) 16.0 , c ) 15 , d ) 16.8 , e ) 16.1
"d = 110 + 140 = 250 m s = 60 * 5 / 18 = 50 / 3 t = 250 * 3 / 50 = 15 sec answer : c"
Break down and solve the equation step by step.
sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 200 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 4 of the days were hot , then what was the price of 1 cup on a hot day ? a ) $ 1.56 , b ) $ 1.88 , c ) $ 2.25 , d ) $ 2.50 , e ) $ 3.25
"6 regular days - - > sales = 6 * 32 * x = 192 x ; 4 hot days - - > sales = 4 * 32 * ( 1.25 x ) = 160 x ; total sales = 192 x + 160 x = 352 x . total cost = 10 * 32 * 0.75 = 240 . profit = 352 x - 240 = 200 - - > x = 1.25 . 1.25 x = ~ 1.56 . answer : a ."
Break down and solve the equation step by step.
find the surface area of a 10 cm * 4 cm * 3 cm brick . ['a ) 154 cm square','b ) 156 cm square','c ) 160 cm square','d ) 164 cm square','e ) none of these']
explanation : surface area of a cuboid = 2 ( lb + bh + hl ) cm square so , surface area of a brick = 2 ( 10 * 4 + 4 * 3 + 3 * 10 ) cm square = 2 ( 82 ) cm square = 164 cm square option d
Provide a detailed solution to the given mathematical problem.
a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 27 km / hr in the same direction . in how much time will the train pass the jogger ? a ) 76 sec , b ) 72 sec , c ) 98 sec , d ) 36 sec , e ) 23 sec
"speed of train relative to jogger = 27 - 9 = 18 km / hr . = 18 * 5 / 18 = 5 m / sec . distance to be covered = 240 + 120 = 360 m . time taken = 360 / 5 = 72 sec . answer : b"
Work through the equation methodically, ensuring clarity at each step.
how many positive integers less than 5,000 are evenly divisible by neither 15 nor 23 ? a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
"integers less than 5000 divisible by 15 5000 / 15 = 333 . something , so 333 integers less than 5000 divisible by 23 5000 / 23 = 238 . # # , so 238 we have double counted some , so take lcm of 15 and 23 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 15 and 23 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4521 answer c ."
Solve the problem systematically, showing each step clearly.
a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2430 ? a ) s . 800 , b ) s . 810 , c ) s . 820 , d ) s . 900 , e ) s . 920
"2430 * 1 / 3 = 810 option b"
Provide a detailed solution to the given mathematical problem.
amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.5 km ? a ) 375 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m
"a 375 m distance covered by amar = 18 / 4.8 ( 1.5 km ) = 3 / 8 ( 1500 ) = 375 m"
Explain the solution process for the given equation.
find the perimetri of trapezium with sides 4 , 6,12 and distance between two parallel side is 3 . ['a ) 27','b ) 26','c ) 28','d ) 25','e ) 24']
1 / 2 * ( 6 + 12 ) * 3 = 27 answer : a
Explain the solution process for the given equation.
in a classroom , the average age of boys ( b ) is g and the average age of girls ( g ) is b . the average age of all is b + g . at the time of calculation , the class teacher , who is 42 years old was also present in the class . can you find the value of b + g ? a ) 8 , b ) 3 , c ) 7 , d ) 9 , e ) 10
a b + g = 8 for b in range ( 199 ) : for g in range ( 199 ) : sum 1 = 2 * b * g + 42 sum 2 = ( b + g ) * ( b + g + 1 ) if ( sum 1 = = sum 2 ) : print ( b , g , sum 1 ) ( b , g ) = ( 35 ) = > b + g = 8
Explain the solution process for the given equation.
80 is increased by 50 % . find the final number . a ) 100 , b ) 110 , c ) 120 , d ) 30 , e ) 160
"final number = initial number + 50 % ( original number ) = 80 + 50 % ( 80 ) = 80 + 40 = 120 . answer c"
Provide a detailed solution to the given mathematical problem.
real - estate salesman z is selling a house at a 30 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 30 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 30 percent discount . salesman y' s final price is what fraction of salesman x' s final price ? a ) 12 / 13 , b ) 11 / 15 , c ) 11 / 17 , d ) 11 / 14 , e ) 11 / 7
"let the retail price be = x selling price of z = 0.70 x selling price of x = 0.70 * 0.80 x = 0.56 x selling price of y = ( ( 0.70 x + 0.56 x ) / 2 ) * 0.70 = 0.63 x * 0.70 = 0.44 x 0.44 x = k * 0.56 x k = 0.44 / 0.56 = 44 / 56 = 11 / 14 answer : d"
Explain the solution process for the given equation.
what is the smallest integer n for which 25 ^ n > 5 ^ 12 ? a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
"to solve , we want to get the bases the same . thus we need to break 25 ^ n into prime factors . 25 ^ n = ( 5 ^ 2 ) ^ n = 5 ^ ( 2 n ) ( remember that when we have a power to a power , we multiply the exponents . ) we can use the new value in the given inequality : 5 ^ ( 2 n ) > 5 ^ 12 since we have the same bases on either side of the inequality we can drop the bases and set up an equation involving just the exponents . 2 n > 12 n > 6 because n is greater than 6 , the smallest integer that satisfies the inequality 25 ^ n > 5 ^ 12 is 7 . the answer is b ."
Provide a detailed solution to the given mathematical problem.
how many squares are there between 2011 to 2300 ? ? ? ? ['a ) 3','b ) 4','c ) 5','d ) 6','e ) 7']
nos . are 2025 , 2116 , 2209 answers is 3 answer : a
Explain the solution process for the given equation.
a shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 2 a rupee . find his net profit or loss percent ? a ) 100 % , b ) 200 % , c ) 250 % , d ) 300 % , e ) 50 %
"the total number of mangoes bought by the shopkeeper be 12 . if he buys 4 a rupee , his cp = 3 he selling at 2 a rupee , his sp = 4 profit = sp - cp = 4 - 2 = 2 profit percent = 2 / 2 * 100 = 100 % answer : a"
Break down and solve the equation step by step.
3 * 14 + 3 * 15 + 3 * 18 + 11 = ? a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 152
"3 * 14 + 3 * 15 + 3 * 18 + 11 = 42 + 45 + 54 + 11 = 152 the answer is e ."
Break down and solve the equation step by step.
a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 9 brown mice in the experiment , how many mice in total are in the experiment ? a ) 39 , b ) 33 , c ) 27 , d ) 21 , e ) 10
"let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 9 = > m = 27 answer c"
Work through the equation methodically, ensuring clarity at each step.
the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 507 sq meters , then what is the width ( in meters ) of the rectangular plot ? a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
"area = l * w = 3 w ^ 2 = 507 w ^ 2 = 169 w = 13 the answer is c ."
Explain the solution process for the given equation.
how many times in a day the hands of a clock are straight ? a ) 21 , b ) 27 , c ) 24 , d ) 22 , e ) 25
"in 12 hours , the hands coincide or are in oppesite direction 22 times . in 24 hours , they are at right angles 22 times . answer is d ."
Explain the solution process for the given equation.
s is a set of 64 consecutive multiples of 4 . if the smallest number in s is 68 , then the greatest number in s is a ) 198 , b ) 297 , c ) 320 , d ) 402 , e ) 405
last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 64 consecutive multiples of 4 . if the smallest number in s is 68 , then the greatest number in s is first term = 68 ; total terms = 64 ; difference = 4 68 + ( 63 ) 4 = 320 ans c
Break down and solve the equation step by step.
price of a book increases 15 % successively ( 2 times ) what is the new price of the book more compared to that of the old price : a ) 32.25 % , b ) 23.34 % , c ) 36 % , d ) 39 % , e ) 29 %
new price is 1.15 * 1.15 * old price = 1.3225 * old price increase in price = 0.3225 * old price % increase = 100 * 0.3225 * old price / old price = 32.25 % answer : a
Solve the problem systematically, showing each step clearly.
a can do a piece of work in 8 days . b can do it in 12 days . with the assistance of c they completed the work in 4 days . find in how many days can c alone do it ? a ) 87 days , b ) 20 days , c ) 16 days , d ) 24 days , e ) 36 days
"c = 1 / 4 - 1 / 8 - 1 / 12 = 1 / 24 = > 24 days answer : d"
Provide a detailed solution to the given mathematical problem.
a shipment of 250 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ? a . b . c . d . e . a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3
probability of choosing one defective phone from a lot of 250 which ontains 84 defective phones is = ( 84 / 250 ) probability of choosing one defective phone from a lot of 249 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 249 ) combined probability of series of events = product of the probabilities = ( 84 / 250 ) * ( 83 / 249 ) 84 / 250 is close to ( 1 / 3 ) and ( 83 / 249 ) = ( 1 / 3 ) so answer is ( 1 / 3 ) * ( 1 / 3 ) = ( 1 / 9 ) answer : d
Break down and solve the equation step by step.
how many three digit numbers n are divisible by 78 or 91 ? a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
"the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well n - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Work through the equation methodically, ensuring clarity at each step.
if 50 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ? a ) 560 , b ) 540 , c ) 520 , d ) 440 , e ) 500
we know 50 % people study biology , therefore the no of people not studying = 100 - 50 = 50 % > therefore the people not studying biology out of a total 880 people are = 50 % of 880 > ( 50 / 100 ) * 880 = 440 people d
Explain the solution process for the given equation.
an ant walks an average of 500 meters in 60 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ? a ) 1.0 , b ) 0.5 , c ) 0.75 , d ) 0.425 , e ) 0.3
"the ant walks an average of 500 meters in 60 minutes 500 meters in 1 hours the beetle walks 15 % less distance = 500 - 75 = 425 meters in 60 minutes 0.425 km in 1 hours speed = 0.425 * 1 = 0.425 km / h i guess option d should be 0.425"
Provide a detailed solution to the given mathematical problem.
12 times a positive integer is more than its square by 36 , then the positive integer is a ) 6 , b ) 10 , c ) 11 , d ) 12 , e ) 14
"explanation : let the number be x . then , 12 x = x 2 + 36 = > x 2 - 12 x + 36 = 0 = > ( x - 6 ) ( x - 6 ) = 0 = > x = 6 answer : a"
Break down and solve the equation step by step.
sides of a rectangular park are in the ratio 4 : 3 and its area is 3750 sq m , the cost of fencing it at 50 ps per meter is ? a ) s . 132.3 , b ) s . 129 , c ) s . 125 , d ) s . 120 , e ) s . 121
"4 x * 3 x = 3750 = > x = 17.7 2 ( 82.3 + 50 ) = 264.6 m 264.6 * 1 / 2 = rs . 132.3 answer : a"
Solve the problem systematically, showing each step clearly.
a and b together have $ 1210 . if of a' s amount is equal to of b' s amount , what is the ratio between a and b ? a ) 2 : 3 , b ) 3 : 2 , c ) 4 : 5 , d ) 5 : 3 , e ) can not be determined
"( 4 / 15 ) a = ( 2 / 5 ) b a = ( ( 2 / 15 ) * ( 15 / 4 ) ) b a = ( 3 / 2 ) b a / b = 3 / 2 a : b = 3 : 2 option b"
Explain the solution process for the given equation.
find the least number which when divided by 38 and 3 leaves a remainder of 1 in each case . a ) 107 , b ) 109 , c ) 111 , d ) 113 , e ) 115
"the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 38 , 3 ) + 1 = 115 . answer : e"
Break down and solve the equation step by step.
a is half good a work man as b and together they finish a job in 18 days . in how many days working alone b finish the job ? a ) 23 , b ) 22 , c ) 27 , d ) 36 , e ) 48
"c 27 wc = 1 : 2 2 x + x = 1 / 18 = > x = 1 / 54 2 x = 1 / 27 = > 27 days"
Work through the equation methodically, ensuring clarity at each step.
if the selling price of 100 articles is equal to the cost price of 40 articles , then the loss or gain percent is : a ) 25 % , b ) 40 % , c ) 60 % , d ) 65 % , e ) 50 %
let c . p . of each article be re . 1 . then , c . p . of 100 articles = rs . 100 ; s . p . of 100 articles = rs . 40 . loss % = 60 / 100 * 100 = 60 % answer : c
Provide a detailed solution to the given mathematical problem.
what is the sum of all possible 3 - digit numbers that can be constructed using the digits 1 , 2 , and 4 if each digit can be used only once in each number ? a ) 1210 , b ) 1221 , c ) 1332 , d ) 1443 , e ) 1554
there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 111 ) + 2 ( 222 ) + 2 ( 444 ) = 1554 the answer is e .
Break down and solve the equation step by step.
the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 47 . what is a possible value for the mean of the distribution ? a ) 46 , b ) 54 , c ) 48 , d ) 49 , e ) 50
the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 47 : { mean } - 3 * { sd } > 47 ; { mean } - 6 > 47 ; { mean } > 53 . answer : b .
Explain the solution process for the given equation.
mahesh can do a piece of work in 40 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ? a ) 45 , b ) 25 , c ) 37 , d ) 41 , e ) 60
"work done by mahesh in 60 days = 20 * 1 / 40 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 1 / 2 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 2 = 60 days answer is e"
Break down and solve the equation step by step.
a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 12 km ? a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 6
"m = 4 s = 2 us = 4 - 2 = 2 d = 12 t = 12 / 2 = 6 answer : e"
Break down and solve the equation step by step.
a rectangular field is to be fenced on three sides leaving a side of 40 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ? a ) 44 ft , b ) 88 ft , c ) 74 ft , d ) 11 ft , e ) 66 ft
"given that length and area , so we can find the breadth . length x breadth = area 40 x breadth = 680 breadth = 17 feet area to be fenced = 2 b + l = 2 ( 17 ) + 40 = 74 feet answer : c ) 74 ft"
Explain the solution process for the given equation.
the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 1250 resolutions ? a ) 1277 m , b ) 1760 m , c ) 1278 m , d ) 1288 m , e ) 1378 v
"in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1250 resolutions . = 1250 * 2 * 22 / 7 * 22.4 = 176000 cm = 1760 m answer : b"
Provide a detailed solution to the given mathematical problem.
the percentage increase in the area of rectangle , if each of its side is increased by 10 % is ? a ) 21 % , b ) 30 % , c ) 25 % , d ) 40 % , e ) 50 %
"let original length = x meters original breadth = y meters original area = xy m ^ 2 new length = 110 x / 100 new breadth = 110 y / 100 = 11 y / 10 new area = 11 x / 10 * 11 y / 10 = 121 xy / 100 m ^ 2 increase percent = 21 xy / 100 * 1 / xy * 100 = 21 % answer is a"
Explain the solution process for the given equation.
what is the probability of getting exactly 2 heads in a single throw of five fair coins ? a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 16 , e ) 11 / 32
"one possible case is hhttt . p ( hhttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 2 = 10 possible cases . p ( 2 heads ) = 10 * 1 / 32 = 5 / 16 the answer is d ."
Provide a detailed solution to the given mathematical problem.
a car traveled from san diego to san francisco at an average speed of 45 miles per hour . if the journey back took twice as long , what was the average speed of the trip ? a ) 30 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 .
"let the time taken be = x one way distance = 45 x total distance traveled = 2 * 45 x = 90 x total time taken = x + 2 x = 3 x average speed = 90 x / 3 x = 30 answer : a"
Provide a detailed solution to the given mathematical problem.
the tax on a commodity is diminished by 19 % and its consumption increased by 15 % . the effect on revenue is ? a ) 2 % , b ) 8.85 % , c ) 5.85 % , d ) 6.85 % , e ) 1 %
"100 * 100 = 10000 81 * 115 = 9315 - - - - - - - - - - - 10000 - - - - - - - - - - - 685 100 - - - - - - - - - - - ? = > 6.85 % decrease answer : d"
Explain the solution process for the given equation.
sandy leaves her home and walks toward ed' s house . two hours later , ed leaves his home and walks toward sandy' s house . the distance between their homes is 52 kilometers , sandy' s walking speed is 6 km / h , and ed' s walking speed is 4 km / h . how many kilometers will sandy walk before she meets ed ? a ) 33 , b ) 34 , c ) 35 , d ) 36 , e ) 37
sandy walks 12 km in the first two hours so there are 40 km remaining . when ed starts walking , they complete a total of 10 km per hour . they will meet four hours after ed starts walking . since sandy walks for 6 hours , she walks 36 km . the answer is d .
Work through the equation methodically, ensuring clarity at each step.
60 % of a number is added to 120 , the result is the same number . find the number ? a ) 300 , b ) 288 , c ) 270 , d ) 129 , e ) 281
"( 60 / 100 ) * x + 120 = x 2 x = 600 x = 300 answer : a"
Break down and solve the equation step by step.
a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 6 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ? a ) 27 , b ) 22 , c ) 24 , d ) 26 , e ) 30
"total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes answer : a"
Provide a detailed solution to the given mathematical problem.
a certain article of clothing was discounted during a special sale to 2 / 5 of its original retail price . when the clothing did n' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ? a ) 50 % , b ) 33.33 % , c ) 25 % , d ) 16.66 % , e ) 12.5 %
"say the original retail price of the item was $ 200 . the price after the first sale = 3 / 5 * $ 200 = $ 120 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 120 - 100 ) / 120 = 1 / 3 = 16.66 % . answer : d ."
Work through the equation methodically, ensuring clarity at each step.
divide $ 1000 among a , b in the ratio 1 : 4 . how many $ that b get ? a ) $ 500 , b ) $ 800 , c ) $ 1000 , d ) $ 200 , e ) $ 750
"sum of ratio terms = 1 + 4 = 5 a = 1000 * 4 / 5 = $ 800 answer is b"
Provide a detailed solution to the given mathematical problem.
a person buys an article at $ 800 . at what price should he sell the article so as to make a profit of 12 % ? a ) 896 , b ) 890 , c ) 990 , d ) 789 , e ) 740
"a 896 cost price = $ 800 profit = 12 % of 800 = $ 96 selling price = cost price + profit = 800 + 96 = 896"
Break down and solve the equation step by step.
nicky and cristina are running a 300 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ? a ) 40 , b ) 50 , c ) 30 , d ) 60 , e ) 45
"the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . c"
Work through the equation methodically, ensuring clarity at each step.
a no . when divided by 125 gives a remainder 40 , what remainder will be obtainedby dividingthe same no . 15 ? a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
"125 + 40 = 165 / 15 = 11 ( remainder ) b"
Work through the equation methodically, ensuring clarity at each step.
in a renowned city , the average birth rate is 8 people every two seconds and the death rate is 6 people every two seconds . estimate the size of the population net increase that occurs in one day . a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 86,400 , e ) 259,200
"every 2 seconds , 2 persons are added ( 8 - 6 ) . every second 1 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 1 = 86400 option d"
Explain the solution process for the given equation.
at an election 2 candidates are participated a candidate got 45 % of votes and defeated by 9000 votes . 83 votes are invalid . find the total polled votes ? a ) 100000 , b ) 85236 , c ) 89562 , d ) 90083 , e ) 95842
"winners votes = 100 - 45 = 55 % invalid votes = 83 polled votes = [ ( 100 * 9000 ) / ( 2 * 55 - 100 ) ] + 83 = 90083 answer is d"
Provide a detailed solution to the given mathematical problem.
a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent q of the distribution is less than m + d ? a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
"d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , q = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d ."
Solve the problem systematically, showing each step clearly.
the average of 45 results is 10 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ? a ) 600 , b ) 480 , c ) 750 , d ) 650 , e ) 560
"23 th result = sum of 45 results - sum of 44 results 10 * 45 - 15 * 22 + 20 * 22 = 450 - 330 + 440 = 560 answer is e"
Break down and solve the equation step by step.
income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 18000 , then find his savings ? a ) rs . 3600 , b ) rs . 3629 , c ) rs . 3279 , d ) rs . 3629 , e ) rs . 3283
"let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 18000 = > x = 3600 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3600 . answer : a"
Solve the problem systematically, showing each step clearly.
a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 5 feet . how many feet does the squirrel travels if the post is 25 feet tall and 3 feet in circumference ? ['a ) 10 feet','b ) 12 feet','c ) 13 feet','d ) 15 feet','e ) 18 feet']
total circuit = 25 / 5 = 5 total feet squirrel travels = 5 * 3 = 15 feet answer : d
Provide a detailed solution to the given mathematical problem.
the present worth of rs . 242 due in 2 years at 10 % per annum compound interest is : a ) rs . 200 , b ) rs . 250 , c ) rs . 240 , d ) rs . 220 , e ) rs . 230
"explanation : present worth of rs . x due t years hence is given by present worth ( pw ) = x / ( 1 + r / 100 ) t present worth ( pw ) = 242 / ( 1 + 10 / 100 ) 2 = 242 / ( 11 / 10 ) 2 = rs . 200 answer : option a"
Break down and solve the equation step by step.
what is the sum of the multiples of 3 from 33 to 60 , inclusive ? a ) 465 , b ) 470 , c ) 452 , d ) 450 , e ) 460
"the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 7 and add 1 . ( 60 / 3 ) - ( 33 / 3 ) + 1 multiply these together so what we show average * total numbers = sum ( 33 + 60 ) / 2 * ( 60 / 3 ) - ( 33 / 3 ) + 1 = sum 93 / 2 * 10 = 465 a"
Solve the problem systematically, showing each step clearly.
a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 190 . find the original price of petrol ? a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 4.2
"price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 190 / 45 = $ 4.2 answer : e ."
Break down and solve the equation step by step.
what is the difference between the largest number and the least number written with the digits 9 , 3 , 5 , 7 ? a ) 6084 , b ) 3788 , c ) 2077 , d ) 2721 , e ) 6174
"explanation : 3579 9753 - - - - - - - - - - - - 6174 answer : e"
Break down and solve the equation step by step.
if 3 x = 9 y = z , what is x + y , in terms of z ? a ) z / 2 , b ) 2 z , c ) z / 3 , d ) 3 z / 5 , e ) 4 z / 9
"3 x = 9 y = z x = z / 3 and y = z / 9 x + y = z / 3 + z / 9 = 4 z / 9 answer is e"
Provide a detailed solution to the given mathematical problem.
of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents z watch all of the shows ? a ) 150 , b ) 108 , c ) 42 , d ) 21 , e ) - 21
oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is z = 3.5 % of 600 , is 21 . d is the correct answer
Work through the equation methodically, ensuring clarity at each step.
amar takes as much time in running 12 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.6 km ? a ) 600 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m
"d 400 m distance covered by amar = 12 / 4.8 ( 1.6 km ) = 2.5 ( 1600 ) = 400 m answer is d"
Provide a detailed solution to the given mathematical problem.
the distance from city a to city b is 180 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 60 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ? a ) 42 , b ) 44 , c ) 46 , d ) 36 , e ) 50
"the time it takes cara to drive to city b is 180 / 30 = 6 hours . dan needs to take less than 5 hours for the trip . dan needs to exceed a constant speed of 180 / 5 = 36 miles per hour . the answer is d ."
Explain the solution process for the given equation.
at a special sale , 9 tickets can be purchased for the price of 6 tickets . if 9 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 9 tickets ? a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 60 % , e ) 66.6 %
"let the price of a ticket be rs . 100 , so 6 tickets cost 600 & 9 tickets cost 900 9 tickets purchased at price of 6 tickets ie . , for 600 , so amount saved s rs . 300 , % of 9 tickets = ( 300 / 900 ) * 100 = 33.3 % answer : b"
Break down and solve the equation step by step.
if grapes are 92 % water and raisins are 20 % water , then how many kilograms did a quantity of raisins , which currently weighs 5 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . ) a ) 50 , b ) 54 , c ) 55 , d ) 56 , e ) 60
"let x be the original weight . the weight of the grape pulp was 0.08 x . since the grape pulp is 80 % of the raisins , 0.08 x = 0.8 ( 5 ) . then x = 50 kg . the answer is a ."
Work through the equation methodically, ensuring clarity at each step.
the weights of 3 bags are in the ratio 4 : 5 : 6 . if the sum of the weights of the heaviest and the lightest bag is 45 kg more than the weight of the third bag , what is the weight of the lightest bag ? a ) 45 kg , b ) 38 kg , c ) 66 kg , d ) 36 kg , e ) of these
let the weights of the three boys be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 45 = > 5 k = 45 = > k = 9 therefore the weight of the lightest boy = 4 k = 4 ( 9 ) = 36 kg . answer : d
Provide a detailed solution to the given mathematical problem.
3 photographers , lisa , mike and norm , take photos of a wedding . the total of lisa and mikes photos is 60 less than the sum of mike' s and norms . if norms photos number 10 more than twice the number of lisa' s photos , then how many photos did norm take ? a ) 40 , b ) 50 , c ) 60 , d ) 110 , e ) 80
l + m = m + n - 60 / n = 2 l + 10 60 = m + n - l - m 60 = n - l 60 = 2 l + 10 - l 50 = l 2 ( 50 ) + 10 = 110 d
Solve the problem systematically, showing each step clearly.
three pipes a , b and c can fill a tank from empty to full in 20 minutes , 20 minutes and 30 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution q in the liquid in the tank after 3 minutes ? a ) 5 / 8 , b ) 6 / 8 , c ) 4 / 8 , d ) 2 / 8 , e ) 3 / 8
"part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 20 + 1 / 20 + 1 / 30 ) = 6 / 15 part filled by b in 3 minutes = 3 / 20 required ratio = 3 / 20 * 15 / 6 = 3 / 8 answer : e"
Solve the problem systematically, showing each step clearly.
in a group of 100 people , 55 have visited iceland and 43 have visited norway . if 61 people have visited both iceland and norway , how many people have visited neither country ? a ) 60 , b ) 61 , c ) 62 , d ) 63 , e ) 64
"this is an example of a standard overlapping sets question . it has no' twists' to it , so you' ll likely find using the overlapping sets formula to be a fairly easy approach . if you' re not familiar with it , then here is the formula : 100 = 55 + 43 - 61 + ( # in neither group ) = 63 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"
Break down and solve the equation step by step.
a 240 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ? a ) 230 m , b ) 240 m , c ) 260 m , d ) 320 m , e ) 330 m
"relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 240 ) / 9 = 500 / 9 x + 240 = 500 x = 260 . c"
Solve the problem systematically, showing each step clearly.
if | x + 3 | = 15 , what is the sum of all the possible values of x ? a ) - 16 , b ) - 12 , c ) - 8 , d ) - 3 , e ) 11
"there will be two cases x + 3 = 15 or x + 3 = - 15 = > x = 12 or x = - 18 sum of both the values will be - 18 + 15 = - 3 answer : d"
Provide a detailed solution to the given mathematical problem.
the cash difference between the selling prices of an book at a profit of 8 % and 16 % is $ 3 . the ratio of the two selling prices is : a ) 55 : 23 , b ) 52 : 33 , c ) 52 : 53 , d ) 27 : 29 , e ) 51 : 34
"let c . p . of the book be $ x . then , required ratio = 108 % of x / 116 % of x = 108 / 116 = 27 / 29 = 27 : 29 d"
Explain the solution process for the given equation.
each of the integers from 0 to 9 , inclusive , is written on a separate slip of blank paper and the ten slips are dropped into a hat . if 4 of the slips are the drawn , without replacement , what is the probability that all 4 have a odd number written on it ? a ) 1 / 12 , b ) 1 / 10 , c ) 1 / 8 , d ) 1 / 42 , e ) 5 / 9
"key is that there is no replacement , so each successive choice will become more skewed towards picking a neg ( i . e . the pool of positives decreases , while the pool of negatives stay the same ) p ( + on 1 st pick ) = 5 / 10 p ( + on 2 nd pick ) = 4 / 9 p ( + on 3 rd pick ) = 3 / 8 p ( + on 4 rd pick ) = 2 / 7 5 / 10 * 4 / 9 * 3 / 8 * 2 / 7 = 1 / 42 d"
Provide a detailed solution to the given mathematical problem.
find the greatest number which on dividing 1428 and 2206 , leaves a reminder of 9 and 13 respectively a ) 125 , b ) 127 , c ) 129 , d ) 131 , e ) 141
"explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 1428 - 9 ) and ( 2206 - 13 ) = hcf ( 1419 , 2193 ) = 129 option c"
Solve the problem systematically, showing each step clearly.
the area of a square garden is q square feet and the perimeter is p feet . if q = 2 p + 33 , what is the perimeter of the garden in feet ? a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
"let x be the length of one side of the square garden . x ^ 2 = 8 x + 33 x ^ 2 - 8 x - 33 = 0 ( x - 11 ) ( x + 3 ) = 0 x = 11 , - 3 p = 4 ( 11 ) = 44 the answer is e ."
Work through the equation methodically, ensuring clarity at each step.
vijay sells a cupboard at 12 % below cost price . had he got rs . 1650 more , he would have made a profit of 12 % . what is the cost price of the cupboard ? a ) 7450 , b ) 14900 , c ) 7400 , d ) 6875 , e ) none of these
"explanation : cost price = 1650 / ( 0.12 + 0.12 ) = 2086 / 0.24 = rs . 6875 answer d"
Work through the equation methodically, ensuring clarity at each step.
how many positive integers less than 350 are there such that they are multiples of 17 or multiples of 18 ? a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40
"350 / 17 = 20 ( plus remainder ) so there are 20 multiples of 17 350 / 18 = 19 ( plus remainder ) so there are 19 multiples of 18 we need to subtract 1 because 17 * 18 is a multiple of both so it was counted twice . the total is 20 + 19 - 1 = 38 the answer is c ."
Explain the solution process for the given equation.
which greatest possible length can be used to measure exactly 15 meter 75 cm , 11 meter 25 cm and 7 meter 65 cm a ) 45 cm , b ) 255 cm , c ) 244 cm , d ) 55 cm , e ) 280 cm
"explanation : convert first all terms into cm . i . e . 1575 cm , 1125 cm , 765 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 255 . option b"
Break down and solve the equation step by step.
a 8 % stock yields 20 % . the market value of the stock is : a ) rs 48 , b ) rs 45 , c ) rs 40 , d ) rs 50 , e ) rs 55
"explanation : for an income of rs . 20 , investment = rs . 100 . for an income of rs 8 , investment = rs . 100 / 20 x 8 = rs 40 market value of rs . 100 stock = rs 40 answer is c"
Work through the equation methodically, ensuring clarity at each step.
when positive integer n is divided by 3 , the remainder is 2 . when n is divided by 5 , the remainder is 5 . how many values less than 100 can n take ? a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5
"a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 0 . . a"
Provide a detailed solution to the given mathematical problem.
a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 80 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ? a ) 71.5 , b ) 72 , c ) 72.5 , d ) 73 , e ) 76.6
"many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 80 kilometers per hour is 1 / 80 hours = 3,600 / 80 seconds = 45 seconds ; time to cover this distance at regular speed is 45 + 2 = 47 seconds = 47 / 3,600 hours = 5 / 383 hours ; so , we get that to cover 1 kilometer 1 / ( 5 / 383 ) hours is needed - - > regular speed 76.6 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e"
Provide a detailed solution to the given mathematical problem.
a light has a rating of 110 watts , it is replaced with a new light that has 30 % higher wattage . how many watts does the new light have ? a ) 143 , b ) 145 , c ) 156 , d ) 134 , e ) 100
"final number = initial number + 30 % ( original number ) = 110 + 30 % ( 110 ) = 110 + 33 = 143 . answer a"
Work through the equation methodically, ensuring clarity at each step.
3 persons invested rs . 9000 in a joint business . the second person invested rs . 1000 more than the first and the third rs . 1000 more than second . after two years , they gained rs . 1800 . how much third person will get ? a ) 400 , b ) 800 , c ) 600 , d ) 1200 , e ) 1000
first persons investment = x second persons investment = x + 1000 third persons investments = x + 2000 x + x + 1000 + x + 2000 = 9000 3 x = 6000 x = 2000 ratio = 2000 : 3000 : 4000 2 : 3 : 4 4 / 9 * 1800 = 800 answer : b
Work through the equation methodically, ensuring clarity at each step.
there is a 5 % chance that tigers will not win at all during the whole season . there is a 5 % chance that federer will not play at all in the whole season . what is the greatest possible probability that the tigers will win and federer will play during the season ? a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 95 %
"there is a 5 % chance that tigers will not win at all during the whole season we can infer that there is 95 % chance tigers will win . similarly there is a 5 % chance that federer will not play at all in the whole season we can also infer that there is 95 % chance that federer will play . answer e"
Work through the equation methodically, ensuring clarity at each step.
youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 12 minutes more to walk to work than to ride his bike to work , then x equals ? a ) 4 , b ) 7 , c ) 10 , d ) 15 , e ) 18
"please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 720 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 7200 - - - - > 40 x = 720 - - > x = 18 . option e"
Explain the solution process for the given equation.
having scored 96 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ? a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24
"explanation : let the average score of the first 18 innings be n 18 n + 96 = 19 ( n + 4 ) = > n = 20 so , average score after 19 th innings = x + 4 = 24 . answer : e"
Explain the solution process for the given equation.
a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 5 per metre of cloth . what is the cost price of one metre of cloth ? a ) 21 , b ) 28 , c ) 90 , d ) 100 , e ) 11
"explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 5 = rs . 100 . answer : d"
Explain the solution process for the given equation.
the maximum number of students among them 1230 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is : a ) 91 , b ) 10 , c ) 1001 , d ) 1911 , e ) none of these
"explanation : required number of students = h . c . f of 1230 and 920 = 10 . answer : b"
Break down and solve the equation step by step.
to fill a tank , 42 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two - fifths of its present ? a ) 102 , b ) 103 , c ) 104 , d ) 105 , e ) 106
"let the capacity of 1 bucket = x . then , the capacity of tank = 42 x . new capacity of bucket = 2 / 5 x therefore , required number of buckets = ( 42 x ) / ( 2 x / 5 ) = ( 42 x ) x 5 / 2 x = 210 / 2 = 105 answer is d ."
Provide a detailed solution to the given mathematical problem.
the list price of an article is rs . 65 . a customer pays rs . 57.33 for it . he was given two successive discounts , one of them being 10 % . the other discount is ? a ) 8 % , b ) 7 % , c ) 10 % , d ) 12 % , e ) 2 %
"option e explanation : 65 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 57.33 x = 2 %"
Explain the solution process for the given equation.
in a division , a student took 42 as divisor instead of 36 . his answer was 24 . the correct answer is - a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38
"x / 42 = 24 . x = 24 * 42 . so correct answer would be , ( 24 * 42 ) / 36 = 38 . answer : e"
Solve the problem systematically, showing each step clearly.
when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.12510168 ? a ) 5 , b ) 6 , c ) 10 , d ) 3 , e ) 8
"for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 9 digits after decimal total no . of decimals = 11 req . no . of digits = ( n - 1 ) = ( 11 - 1 ) = 10 answer : c"
Explain the solution process for the given equation.
two numbers a and b are such that the sum of 5 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b . a ) 2 : 3 , b ) 1 : 1 , c ) 3 : 4 , d ) 4 : 3 , e ) 5 : 5
"5 / 100 a + 4 / 100 b = 2 / 3 ( 6 / 100 a + 8 / 100 b ) = > 1 / 20 a + 1 / 25 b = 1 / 25 a + 4 / 75 b = > ( 1 / 20 - 1 / 25 ) b = 1 / 25 a + 4 / 75 b ( 1 / 20 - 1 / 25 ) a = ( 4 / 75 - 1 / 25 ) b 1 / 100 a = 1 / 75 b a / b = 100 / 75 = 4 / 3 req ratio = 4 : 3 answer d"
Solve the problem systematically, showing each step clearly.
if an object travels at three feet per second , how many feet does it travel in one hour ? a ) 3488 , b ) 10800 , c ) 12788 , d ) 1800 , e ) 2881
explanation : if an object travels at 2 feet per second it covers 3 x 60 feet in one minute , and 3 x 60 x 60 feet in one hour . answer = 10800 answer : b ) 10800