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Explain the solution process for the given equation. | x and y began business with rs . 10000 and rs . 8000 after 6 months , x advances rs . 2000 and y advances rs . 2000 more . at the end of the year , their profits amounted to rs . 2000 find the share of x and y respectively . a ) 10001000 , b ) 9001100 , c ) 1200800 , d ) 8001200 , e ) 1100 , 900 | ( 10 * 6 + 12 * 6 ) : ( 8 * 6 + 10 * 6 ) 11 : 9 x share = 11 / 20 * 2000 = 1100 . y share = 9 / 20 * 2000 = 900 . x and y share respectively is 1100 , 900 . answer : e |
Solve the problem systematically, showing each step clearly. | at what price must an article costing rs . 85.5 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ? a ) 122.5 , b ) 142.5 , c ) 162.5 , d ) 182.5 , e ) 112.5 | "cp = 85.50 sp = 85.5 * ( 125 / 100 ) = 106.875 mp * ( 95 / 100 ) = 106.875 mp = 112.5 answer : e" |
Work through the equation methodically, ensuring clarity at each step. | two friends plan to walk along a 33 - km trail , starting at opposite ends of the trail at the same time . if friend p' s rate is 20 % faster than friend q' s , how many kilometers will friend p have walked when they pass each other ? a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19 | "if q complete x kilometers , then p completes 1.2 x kilometers . x + 1.2 x = 33 2.2 x = 33 x = 15 then p will have have walked 1.2 * 15 = 18 km . the answer is d ." |
Provide a detailed solution to the given mathematical problem. | p and q started a business investing rs 10000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively . a ) 2 : 7 , b ) 2 : 6 , c ) 17 : 6 , d ) 2 : 3 , e ) 7 : 8 | "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 10000 : 15000 = 10 : 15 = 2 : 3 option d" |
Solve the problem systematically, showing each step clearly. | in a sports club with 30 members , 16 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ? a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | "let x play both badminton and tennis so 16 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 16 - x ) + ( 19 - x ) + x + 2 = 30 37 - 2 x + x = 30 37 - x = 30 x = 7 so 7 members play both badminton and tennis . a" |
Work through the equation methodically, ensuring clarity at each step. | a $ 84.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ? a ) 15 % , b ) 20 % , c ) 25 % , d ) 29 % , e ) 80 % | "listed selling price of chair = 84.95 $ discounted selling price of chair = 59.95 $ discount = 84.95 - 59.95 = 25 $ % decrease in price of chair = ( 25 / 84.95 ) * 100 % = 29 % approx answer d" |
Break down and solve the equation step by step. | an artist wishes to paint a circular region on a square poster that is 3 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ? a ) 1 / pi , b ) sqrt ( 2 / pi ) , c ) sqrt ( 4.5 / pi ) , d ) 2 / sqrt ( pi ) , e ) pi / 2 | "area of the poster is 3 x 3 = 9 1 / 2 the area = 4.5 pi * r ^ 2 = 4.5 r ^ 2 = 4.5 / pi r = sqrt ( 4.5 / pi ) answer ( c )" |
Break down and solve the equation step by step. | jim is able to sell a hand - carved statue for $ 670 which was a 25 % profit over his cost . how much did the statue originally cost him ? a ) $ 496.30 , b ) $ 536.00 , c ) $ 555.40 , d ) $ 574.90 , e ) $ 588.20 | "670 = 1.25 * x x = 670 / 1.25 = 536 $ 536 , which is ( b ) ." |
Explain the solution process for the given equation. | by selling 10 pens for a rupee a woman loses 18 % . how many for a rupee should he sell in order to gain 30 % ? a ) 12 , b ) 14 , c ) 45 , d ) 6 , e ) 7 | "d 82 % - - - 10 130 % - - - ? 82 / 130 * 10 = 6" |
Solve the problem systematically, showing each step clearly. | the sum of the present age of henry and jill is 41 . what is their present ages if 7 years ago henry was twice the age of jill ? a ) and 25 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these | let the age of jill 7 years ago be x , age of henry be 2 x x + 7 + 2 x + 7 = 41 x = 9 present ages will be 16 and 25 answer : a |
Break down and solve the equation step by step. | a reduction of 15 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 1200 , what is the reduced price for kg ? a ) 43 , b ) 55 , c ) 35 , d ) 45 , e ) 40 | "1200 * ( 15 / 100 ) = 180 - - - - 4 ? - - - - 1 = > rs . 45 answer : d" |
Work through the equation methodically, ensuring clarity at each step. | at a florist shop on a certain day , all corsages sold for either $ 25 or $ 40 . if 8 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store' s revenue from corsages that day would have been reduced by 40 percent . what was the store' s actual revenue from corsages that day ? a ) $ 200 , b ) $ 40... | "i am doing it elaborately , hope it will help you . let , no . of corsages @ $ 25 = x , no . of corsages @ $ 40 = y and revenue = r so , 25 x + 40 y = r . . . . . . . . . ( 1 ) now , given the situation , 25 ( x + 8 ) + 40 ( y - 8 ) = r - . 4 r = > 25 x + 200 + 40 y - 320 = . 6 r = > 25 x + 40 y = . 8 r + 120 . . . . ... |
Provide a detailed solution to the given mathematical problem. | which greatest possible length can be used to measure exactly 12 meter 15 cm , 10 meter 15 cm and 10 meter 65 cm a ) 45 cm , b ) 25 cm , c ) 4 cm , d ) 5 cm , e ) 50 cm | "explanation : convert first all terms into cm . i . e . 1215 cm , 1015 cm , 1065 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 5 . option d" |
Explain the solution process for the given equation. | john is building a rectangular fence around a garden . the length will be 5 feet shorter than its width . if the total area of the garden is 176 square feet , what is the length of the diagonal ( in feet ) ? ['a ) between 18 and 19','b ) between 19 and 20','c ) between 20 and 21','d ) between 21 and 22','e ) between 22... | to solve this , we first need to set up an equation for the area of the garden . if x is the width , then we have x ( x - 5 ) = 176 . by putting the equation in standard form , we get x ^ 2 - 5 x - 176 = 0 . by using the quadratic formula , we get roots of - 11 and 16 . we know that x is the width , and x - 5 is the le... |
Provide a detailed solution to the given mathematical problem. | if k is an integer and 0.00010101 x 10 ^ k is greater than 1000 , what is the least possible value of k ? a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | "0.00010101 * 10 ^ k > 1000 we need to move the decimal point to the right 7 places to get 1010.1 this is equivalent to multiplying by 10 ^ 7 . the answer is b ." |
Work through the equation methodically, ensuring clarity at each step. | length of a rectangular plot is 30 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ? a ) 46 m , b ) 60 m , c ) 65 m , d ) 78 m , e ) 80 m | "let breadth = x metres . then , length = ( x + 30 ) metres . perimeter = 5300 / 26.5 m = 200 m . 2 [ ( x + 30 ) + x ] = 200 2 x + 30 = 100 2 x = 70 x = 35 . hence , length = x + 30 = 65 m c" |
Provide a detailed solution to the given mathematical problem. | x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 32 days . how long will y take to complete the work ? a ) 10 , b ) 40 , c ) 15 , d ) 18 , e ) 20 | "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 32 days whole work will be done by y in 32 * 5 / 4 = 40 days answer is b" |
Explain the solution process for the given equation. | a person bought 110 glass bowls at a rate of rs . 10 per bowl . he sold 100 of them at rs . 14 and the remaining broke . what is the percentage gain for a ? a ) 40 , b ) 300 / 11 , c ) 243 / 7 , d ) 279 / 11 , e ) 279 / 8 | "cp = 110 * 10 = 1100 and sp = 100 * 14 = 1400 gain % = 100 * ( 1400 - 1100 ) / 1100 = 300 / 11 answer : b" |
Work through the equation methodically, ensuring clarity at each step. | a retailer buys 100 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ? a ) 110 , b ) 175 , c ) 212 , d ) 218 , e ) 220 | "let the market price of each pen be $ 1 then , cost price of 100 pens = $ 36 selling price of 100 pens = 99 % of $ 100 = $ 99 profit % = ( ( 63 * 100 ) / 36 ) % = 175 % answer b" |
Work through the equation methodically, ensuring clarity at each step. | 100 white and black tiles will be used to form a 20 x 20 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ? a ) 75 , b ) 70 , c ) 85 , d ) 90 , e ) 95 | "answer = b please refer diagram below 90 - 20 = 70" |
Solve the problem systematically, showing each step clearly. | a cycle is bought for rs . 1000 and sold for rs . 2000 , find the gain percent ? a ) 11 , b ) 20 , c ) 100 , d ) 77 , e ) 12 | "1000 - - - - 1000 100 - - - - ? = > 100 % answer : c" |
Solve the problem systematically, showing each step clearly. | the area of a triangle will be when a = 3 m , b = 4 m , c = 5 m , a , b , c being lengths of respective sides ? a ) 3 , b ) 6 , c ) 4 , d ) 9 , e ) 1 | s = ( 3 + 4 + 5 ) / 2 = 6 answer : b |
Solve the problem systematically, showing each step clearly. | a bag contains 4 white marbles and 4 black marbles . if each of 4 girls and 4 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? a ) 1 / 35 , b ) 1 / 9 , c ) 1 / 10 , d ) 1 / 20 , e ) 1 / 30 | "first , total ways to select for all boys and girls , i . e 8 ! / ( 4 ! * 4 ! ) = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1 * 4 * 3 * 2 * 1 = 70 then there are one two way girls can have all same colors , either white or black . the number of ways in which 4 girls can select 4 white balls = 4 c 4 = 1 the number of... |
Break down and solve the equation step by step. | find a number such that when 15 is subtracted from 7 times the number , the result is 10 more than twice the number . a ) 1 , b ) 4 , c ) 5 , d ) 0 , e ) 3 | let the number be x . then , 7 x - 15 = 2 x + 10 = > 5 x = 25 = > x = 5 . hence , the required number is 5 . answer is c . |
Solve the problem systematically, showing each step clearly. | the average weight of a group of 30 friends increases by 10 kg when the weight of additional 30 friends was added . if average weight of the whole group after including the additional 30 members is 40 kg , what is the average weight of the additional friends ? a ) 50 kg , b ) 60 kg , c ) 61 kg , d ) 62 kg , e ) 91 kg | let a = avg . wt . of additional 30 friends original total weight = ( 30 friends ) ( 30 kg avge ) = 900 kg ( 900 + 30 a ) / ( 30 + 30 ) = 40 kg avge a = 50 kg answer - a |
Solve the problem systematically, showing each step clearly. | in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the b... | "ratio of 2 bedroom apartment : 1 bedroom apartment = 2800 : 8400 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : c" |
Explain the solution process for the given equation. | the present worth of $ 3600 due in 2 years at 20 % per annum compound interest is ? a ) $ 1200 , b ) $ 1850 , c ) $ 2010 , d ) $ 3200 , e ) $ 2500 | present worth = 3600 / ( 1 + 20 / 100 ) ^ 2 = 3600 * 5 / 6 * 5 / 6 = $ 2500 answer is e |
Work through the equation methodically, ensuring clarity at each step. | $ 8,000 is deposited in a savings account that pays 12 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ? a ) $ 8288.55 , b ) $ 8985.10 , c ) $ 8988.80 , d ) $ 8977.14 , e ) $ 8964.95 | "this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 12 / 2 = 6 % now , ca = 8000 ( 1 + 6 / 100 ) ^ 2 = $ 8988.80 hence answer is c" |
Explain the solution process for the given equation. | a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint e , in gallons , that must be purchased in order to measure... | "given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , l... |
Work through the equation methodically, ensuring clarity at each step. | 2 , 3 , 6 , 15 , _ , 123 ? a ) 42 , b ) 38 , c ) 28 , d ) 29 , e ) 11 | answer : a |
Explain the solution process for the given equation. | how many seconds will a 600 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ? a ) 48 , b ) 36 , c ) 26 , d ) 11 , e ) 18 | "explanation : here distance d = 600 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 36 sec . answer : b" |
Work through the equation methodically, ensuring clarity at each step. | a card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox . find the total number of pins used . a ) 135 , b ) 136 , c ) 137 , d ) 138 , e ) 139 | ( 35 * 4 ) - 4 = 136 answer : b |
Explain the solution process for the given equation. | two trains a and b start simultaneously in the opposite direction from two points p and q and arrive at their destinations 16 and 9 hours respectively after their meeting each other . at what speed does the second train b travel if the first train travels at 120 km / h a ) 334 , b ) 160 , c ) 387 , d ) 278 , e ) 112 | answer : b ) 160 km / h |
Explain the solution process for the given equation. | the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 5 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of t... | "to get 40 points as end of season we need another 35 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 option c = 8 * 3 + 7 * 1 = 31 option d = 9 * 3 + 6 * 1 = 33 option e = 10 * 3 + 5 * 1 = 35 hence option e - 10" |
Provide a detailed solution to the given mathematical problem. | tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 6 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the ... | "tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 4 / 6 ) = 1 / 2 hours peter worked for 3 / 2 hours so he painted 3 / 2 * 1 / 3 = 1 / 2 of the room . ... |
Break down and solve the equation step by step. | an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 4000 , what will be the difference between q and r' s share ? a ) 2788 , b ) 5000 , c ) 7282 , d ) 2782 , e ) 2729 | "4 - - - 4000 5 - - - ? = > 5000 answer : b" |
Provide a detailed solution to the given mathematical problem. | a , b and c can do a piece of work in 24 , 30 and 40 days respectively . they start the work together but c leaves 4 days before the completion of the work . in how many days is the work done ? a ) 11 , b ) 5 , c ) 70 , d ) 11 , e ) 13 | x / 24 + x / 30 + x / 40 = 1 x = 11 days answer : d |
Break down and solve the equation step by step. | a woman swims downstream 54 km and upstream 6 km taking 6 hours each time , what is the speed of the woman in still water ? a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | "54 - - - 6 ds = 9 ? - - - - 1 6 - - - - 6 us = 1 ? - - - - 1 m = ? m = ( 9 + 1 ) / 2 = 5 answer : d" |
Solve the problem systematically, showing each step clearly. | 2 trains in same direction at 50 km / hr , 32 km / hr . a man in slower train observes 15 sec elapse before the faster train completely passed by him what is length of faster train ? a ) 65 meters , b ) 75 meters , c ) 85 meters , d ) 95 meters , e ) 55 meters | relative speed = 18 k / hr = 5 m / sec distance covered = length of faster train = 5 * 15 = 75 meters answer : b |
Provide a detailed solution to the given mathematical problem. | in an examination 35 % of the students passed and 455 failed . how many students appeared for the examination ? a ) 540 , b ) 400 , c ) 700 , d ) 650 , e ) 840 | "let the number of students appeared be x then , 65 % of x = 455 65 x / 100 = 455 x = 455 * 100 / 65 = 700 answer is c" |
Explain the solution process for the given equation. | in a division sum , the remainder is 4 and the divisor is 3 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is : a ) 53 , b ) 58 , c ) 51 , d ) 60 , e ) 62 | "diver = ( 4 * 3 ) + 2 = 14 4 * quotient = 14 quotient = 3.5 dividend = ( divisor * quotient ) + remainder dividend = ( 14 * 3.5 ) + 4 = 53 a" |
Solve the problem systematically, showing each step clearly. | a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 2 days . b can do the work alone in ? a ) 3 hours , b ) 6 hours , c ) 7 hours , d ) 4 hours , e ) 8 hours | "b 6 hours suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 2 6 / x = 1 / 2 = > x = 12 so , b takes 6 hours to finish the work ." |
Solve the problem systematically, showing each step clearly. | a certain industrial loom weaves 0.132 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ? a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118 | "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.132 : 15 : : 1 : x = > 0.132 * x = 15 = > x = 15 / 0.132 = > x = 114 answer : a" |
Work through the equation methodically, ensuring clarity at each step. | mary' s income is 60 % more than tim' s income and tim' s income is 20 % less than juan' s income . what % of juan' s income is mary' s income . a ) 128 % , b ) b . 120 % , c ) 96 % , d ) 80 % , e ) 64 % | even i got 96 % j = 100 t = 100 * 0.8 = 80 m = 80 * 1.6 = 128 if mary' s income is x percent of j m = j * x / 100 x = m * 100 / j = 128 * 100 / 100 = 128 ans : a |
Break down and solve the equation step by step. | two trains 151 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ? a ) 7.19 , b ) 7.18 , c ) 7.16 , d ) 7.84 , e ) 7.12 | "t = ( 151 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.84 answer : d" |
Provide a detailed solution to the given mathematical problem. | in an office , totally there are 5200 employees and 45 % of the total employees are males . 50 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ? a ) 1040 , b ) 1170 , c ) 1150 , d ) 4160 , e ) none of these | "number of male employees = 5200 * 45 / 100 = 2340 required number of male employees who are less than 50 years old = 4160 * ( 100 - 50 ) % = 2340 * 50 / 100 = 1170 . answer : b" |
Solve the problem systematically, showing each step clearly. | sum of 24 odd numbers is ? a ) 572 , b ) 573 , c ) 574 , d ) 575 , e ) 576 | "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 24 odd numbers = 24 ^ 2 = 576 answer : e" |
Solve the problem systematically, showing each step clearly. | income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 16000 , then find his savings ? a ) 3600 , b ) 3607 , c ) 3200 , d ) 3602 , e ) 3603 | "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 16000 = > x = 3200 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3200 . answer : c" |
Break down and solve the equation step by step. | a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase e in sales ? a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 % | "last year' s sales = $ 320 million ; this year' s sales = $ 385 million ; increase e = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ." |
Provide a detailed solution to the given mathematical problem. | if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value s of z - x ? a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + o... |
Break down and solve the equation step by step. | a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20 % while buying and by 10 % while selling . what is his percentage profit ? a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 20 % , e ) ca n' t be calculated | "the owner buys 100 kg but actually gets 120 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 120 - 90 ) / 90 * 100 = 20 % answer : d ." |
Solve the problem systematically, showing each step clearly. | the effective annual rate of interest corresponding to a nominal rate of 6 % per annum payable half - yearly is ? a ) 6.99 % , b ) 6.89 % , c ) 6.08 % , d ) 6.09 % , e ) 6.19 % | "amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 3 / 100 ) 2 ] = rs . 106.09 effective rate = ( 106.09 - 100 ) = 6.09 % answer : d" |
Solve the problem systematically, showing each step clearly. | if $ 120 invested at a certain rate of simple interest amounts to $ 160 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ? a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 250 | "120 amounts to 160 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 160 120 + 120 * ( r / 100 ) * ( 3 ) = 160 = > r = 100 / 9 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) 250 answer is e ." |
Solve the problem systematically, showing each step clearly. | an inspector rejects 10 % of the meters as defective . how many will he examine to reject 20 ? a ) a ) 100 , b ) b ) 120 , c ) c ) 250 , d ) d ) 200 , e ) e ) 160 | "then , 10 % of x = 20 ( 10 / 100 ) x = 20 x = ( 20 * 100 * ) / 10 = 200 answer is d" |
Solve the problem systematically, showing each step clearly. | how long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length ? a ) 28 , b ) 41.25 , c ) 55 , d ) 18 , e ) 12 | "t = ( 660 + 165 ) / 72 * 18 / 5 t = 41.25 answer : b" |
Work through the equation methodically, ensuring clarity at each step. | the length of the bridge , which a train 140 meters long and travelling at 45 km / hr can cross in 30 seconds , is ? a ) 328 , b ) 279 , c ) 235 , d ) 288 , e ) 211 | speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 140 + x ) / 30 = 25 / 2 = = > 2 ( 140 + x ) = 750 = = > x = 235 m . answer : c |
Break down and solve the equation step by step. | what is 2 2 / 3 - 1 1 / 4 divided by 1 / 4 - 1 / 6 ? a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 6 , d ) 17 / 1 , e ) 51 / 4 | "2 2 / 3 - 1 1 / 4 = 8 / 3 - 5 / 4 = ( 32 - 15 ) / 12 = 17 / 12 1 / 4 - 1 / 6 = ( 6 - 4 ) / 24 = 2 / 24 = 1 / 12 so 17 / 12 / 1 / 12 = 17 / 12 * 12 = 17 / 1 answer - d" |
Break down and solve the equation step by step. | 17 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ? a ) 34 , b ) 87 , c ) 30 , d ) 99 , e ) 77 | "3 w = 2 m 17 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 17 * 21 * 8 = 14 * x * 6 x = 34 answer : a" |
Explain the solution process for the given equation. | a merchant marks his goods up by 20 % and then offers a discount of 5 % on the marked price . what % profit does the merchant make after the discount ? a ) 8 % , b ) 6 % , c ) 21 % , d ) 14 % , e ) 17 % | "let the price be 100 . the price becomes 120 after a 20 % markup . now a discount of 5 % on 120 . profit = 114 - 100 14 % answer d" |
Break down and solve the equation step by step. | an alloy weighing 20 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ? a ) 6 , b ) 9 , c ) 12 , d ) 76 , e ) 48 | "in 24 ounces , gold is 20 * ( 70 / 100 ) = 14 ounces . now we add x ounces of pure gold to make it 90 % gold . so 14 + x = ( 24 + x ) * 90 / 100 = > x = 76 . answer is d ." |
Provide a detailed solution to the given mathematical problem. | bird is flying 120 km / hr between b to r . two trains at b to r at 60 kmph . the distance traveled by the bird before it is killed ? a ) 90 kms . , b ) 100 kms . , c ) 110 kms . , d ) 120 kms . , e ) 130 kms . | it will depend on the distance between b and r . if distance between b and r is 120 kms , time taken by trains before collision = 120 / ( 60 + 60 ) = 1 hr distance traveled by bird in 1 hr = 120 kms . so the distance traveled by the bird before it is killed = 120 kms . answer : d |
Break down and solve the equation step by step. | the perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ? a ) 28 cm 2 , b ) 27 cm 2 , c ) 29 cm 2 , d ) 25 cm 2 , e ) 35 cm 2 | "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 20 / 2 = 25 cm 2 answer : d" |
Provide a detailed solution to the given mathematical problem. | during the first two weeks of january , the total rainfall in springdale was 30 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ? a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 18 inches | "total rainfall in 2 weeks = 18 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 18 inches x = 12 and 1.5 x = 18 rainfall during second week = 18 inches option e" |
Work through the equation methodically, ensuring clarity at each step. | what is the distance covered by a train if it travels with a speed of 150 kmh for 8 hours ? a ) 1000 km , b ) 700 km , c ) 800 km , d ) 1400 km , e ) 1200 km | "distance = time x speed distance = 150 x 8 = 1200 answer : e" |
Break down and solve the equation step by step. | if the least common multiple of two prime numbers x and y is 77 , where x > y , then the value of 2 x + y is a ) 11 , b ) 17 , c ) 21 , d ) 29 , e ) 33 | "lcm ( x , y ) = 77 and both x an y are prime . the only values of x and y can be 11 and 7 ( x = 11 and y = 7 ) 2 x + y = 2 * 11 + 7 = 29 correct option : d" |
Explain the solution process for the given equation. | what is the probability that company g' s advertisement will be one of the first two be shown during the first commercial break ? a ) 1 / 225 , b ) 1 / 30 , c ) 1 / 15 , d ) 2 / 15 , e ) 4 / 15 | g 1 / 15 + ( 14 / 15 ) * 1 / 14 = 2 / 15 d |
Break down and solve the equation step by step. | how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 24 percent alcohol ? a ) 7 / 2 , b ) 5 , c ) 20 / 3 , d ) 100 / 19 , e ) 39 / 4 | "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 24 % of ( 100 + x ... |
Work through the equation methodically, ensuring clarity at each 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 6 km ? a ) 3 , b ) 5 , c ) 6 , d ) 67 , e ) 7 | "m = 4 s = 2 us = 4 - 2 = 2 d = 6 t = 6 / 2 = 3 answer : a" |
Break down and solve the equation step by step. | the average weight of 10 persons increases by 6.3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? a ) 176 kg , b ) 80 kg , c ) 185 kg , d ) 90 kg , e ) 128 kg | "solution total weight increased = ( 10 x 6.3 ) kg = 63 kg . weight of new person = ( 65 + 63 ) kg = 128 kg . answer e" |
Break down and solve the equation step by step. | what will be the remainder when ( 27 ^ 27 ) + 27 is divided by 28 ? a ) 22 , b ) 20 , c ) 24 , d ) 26 , e ) 28 | "x ^ n + 1 will be divisible by x + 1 only when n is odd 27 ^ 27 + 1 will be divisible by 27 + 1 ( 27 ^ 27 + 1 ) + 26 , when divided by 28 will give 26 as remainder answer is d" |
Provide a detailed solution to the given mathematical problem. | a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 60 % ? a ) 800 , b ) 882 , c ) 772 , d ) 652 , e ) 271 | "cost price = rs . 500 profit = 60 % of 500 = rs . 300 selling price = cost price + profit = 500 + 300 = 800 answer : a" |
Explain the solution process for the given equation. | a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 570 pounds after processing , how many pounds did it weigh before processing ? a ) 191 , b ) 355 , c ) 737 , d ) 876 , e ) 1,560 | "let weight of side of beef before processing = x ( 65 / 100 ) * x = 570 = > x = ( 570 * 100 ) / 65 = 876 answer d" |
Explain the solution process for the given equation. | 5216 x 51 = ? a ) 212016 , b ) 266016 , c ) 266436 , d ) 216314 , e ) 216318 | "normal way of multiplication may take time . here are one alternative . 5216 x 51 = ( 5216 x 50 ) + 5216 = ( 5216 x 100 ) / 2 + 5216 = 521600 / 2 + 5216 = 260800 + 5216 = 266016 answer is b" |
Provide a detailed solution to the given mathematical problem. | a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 200 . find the total worth of the stock ? a ) 20029 , b ) 20000 , c ) 10000 , d ) 20027 , e ) 20026 | "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 200 = > x = 10000 answer : c" |
Explain the solution process for the given equation. | a bicycle wheel has a diameter of 0.66 m . how many complete revolutions does it make in 1 km ? a ) 246 , b ) 448 , c ) 1408 , d ) 482 , e ) 223 | "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.66 m ) = 482.5 . hence 482 complete revolutions . answer d" |
Provide a detailed solution to the given mathematical problem. | of the families in city x in 2001 , 25 percent owned a personal computer . the number of families in city x owning a computer in 2008 was 15 percent greater than it was in 2001 , and the total number of families in city x was 6 percent greater in 2008 than it was in 2001 . what percent of the families in city x owned a... | "say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 25 number of families owning computer in 1998 = 25 * 115 / 100 = 28.75 number of families in 1998 = 106 the percentage = 28.75 / 106 * 100 = 27.12 % . answer : a" |
Provide a detailed solution to the given mathematical problem. | in a clothing store , there are 6 different colored neckties ( red , orange , yellow , green , blue , and indigo ) and 4 different colored shirts ( red , orange , yellow , green , blue , and indigo ) that must be packed into boxes for gifts . if each box can only fit one necktie and one shirt , what is the probability ... | 4 ties and 4 shirts . . . red tie can take any of 4 shirts . . orange can take any of the remaining 3 shirts yellow any of remaining 2 . . and so on till last indigo chooses the 1 remaining . . total ways = 4 * 3 * 2 * 1 = 24 out of this 720 , only 1 way will have same colour tie and shirt . . prob = 1 / 720 b |
Explain the solution process for the given equation. | last year sandy saved 6 % of her annual salary . this year , she made 10 % more money than last year , and she saved 9 % of her salary . the amount saved this year was what percent of the amount she saved last year ? a ) 140 % , b ) 152 % , c ) 165 % , d ) 176 % , e ) 190 % | let last year' s salary be x . last year , sandy save 0.06 x this year , sandy saved 0.09 * 1.1 x = 0.099 x 0.099 x / 0.06 x = 99 / 60 = 1.65 = 165 % the answer is c . |
Explain the solution process for the given equation. | after decreasing 20 % in the price of an article costs rs . 200 . find the actual cost of an article ? a ) 280 , b ) 250 , c ) 260 , d ) 270 , e ) 300 | "cp * ( 80 / 100 ) = 200 cp = 2.5 * 100 = > cp = 250 answer : b" |
Explain the solution process for the given equation. | find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 100 of money ? a ) 1500 , b ) 6000 , c ) 2500 , d ) 1400 , e ) 2000 | "p = 100 ( 100 / 10 ) 2 = > p = 2000 answer : e" |
Provide a detailed solution to the given mathematical problem. | exactly 10 % of the reporters for a certain wire service cover local politics in country x . if 30 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ? a ) 20 % , b ) 42 % , c ) 44 % , d ) 85 % , ... | "you are correct . people who cover local politics are a subset of people who cover politics . 30 % of reporters who cover politics do not cover local politics so 70 % do cover local politics . reporters covering local politics = 70 % of reporters covering politics = 10 % of all reporters reporters covering politics / ... |
Work through the equation methodically, ensuring clarity at each step. | in a recent head - to - head run - off election , 10,000 absentee ballets were cast . 2 / 3 of the absentee ballets were thrown out and 2 / 5 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ? a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000 | "1 / 3 * 3 / 5 ( total absentee votes ) = 1 / 5 ( total votes ) = 1 / 5 * 10000 = 2000 answer is a" |
Solve the problem systematically, showing each step clearly. | a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 400 feet . what is its area , in square feet ? a ) 76,800 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800 | "you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for s... |
Provide a detailed solution to the given mathematical problem. | in one alloy there is 12 % chromium while in another alloy it is 10 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy . a ) 8.8 % , b ) 9 % , c ) 9.2 % , d ) 8.6 % , e ) 10.6 % | "the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.12 * 15 + 0.10 * 35 = 5.3 kg , so the percentage is 5.3 / 50 * 100 = 10.6 % . answer : e ." |
Solve the problem systematically, showing each step clearly. | in a division , a student took 48 as divisor instead of 36 . his answer was 24 . the correct answer is - a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38 | "x / 48 = 24 . x = 24 * 48 . so correct answer would be , ( 24 * 48 ) / 36 = 32 . answer : b" |
Explain the solution process for the given equation. | an amount of rs . 3120 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ? a ) 720 , b ) 360 , c ) 250 , d ) 280 , e ) 290 | "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of c = 3 / 13 * 3120 = rs . 720 an... |
Solve the problem systematically, showing each step clearly. | a part - time employee whose hourly wage was increased by 15 percent decided to reduce the number of hours worked per week so that the employee' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ? a ) 9 , b ) 13.04 , c ) 10 , d ) 11 , e ) 12 | "let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.15 x now we need to find number of hours worked so that x * y = 1.15 x * z i . e z = 1 / 1.15 y % decrease = ( y - 1 / 1.15 y ) / y * 100 = 13.04 % thus my answer is b ." |
Break down and solve the equation step by step. | sally , mark , sarah , steve and jim are inheriting the money from their grandmother . she left them $ 527500 to split equally between all of them . if the money is split equally , how much money will each person receive ? a ) $ 135875 , b ) $ 52700 , c ) $ 127900 , d ) $ 105500 , e ) $ 105000 | there are 5 people inheriting the money . we have to take the total of the inheritance and divide it by 5 for each person receiving money . $ 527500 / 5 = $ 105500 . therefore the correct answer is d . |
Provide a detailed solution to the given mathematical problem. | a batsman in his 11 th inning makes a score of 69 and their by increasing his average by 1 . what is his average after the 11 th inning ? a ) 58 , b ) 59 , c ) 68 , d ) 69 , e ) 78 | "10 x + 69 = 11 ( x + 1 ) x = 58 + 1 = 59 answer : b" |
Break down and solve the equation step by step. | a train speeds past a pole in 15 sec and a platform 150 m long in 25 sec , its length is ? a ) 100 , b ) 150 , c ) 160 , d ) 225 , e ) 180 | "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 150 ) / 25 = x / 15 = > x = 225 m . answer : option d" |
Work through the equation methodically, ensuring clarity at each step. | the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 10 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait... | after passing the hiker the cyclist travels for 5 minutes at a rate of 10 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 6 miles . in those 5 mins the hiker travels a distance of 1 / 2 miles . so the hiker still has to cover 1 / 2 miles to meet the waiting cyclist . the hiker will need 15 / 2 mins... |
Explain the solution process for the given equation. | the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 50,000 , how much profit did the business make ? a ) $ 80,000 , b ) $ 100,000 , c ) $ 120,000 , d ) $ 150,000 , e ) $ 200,000 | let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = 50000 p = $ 80,000 the answer is a . |
Explain the solution process for the given equation. | in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is a ) 20 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m | "explanation : each row contains 12 plants . there are 11 gapes between the two corner trees ( 11 x 2 ) metres and 1 metre on each side is left . therefore length = ( 22 + 2 ) m = 24 m . answer : c" |
Explain the solution process for the given equation. | sides of a rectangular park are in the ratio 3 : 2 and its area is 2400 sq m , the cost of fencing it at 50 ps per meter is ? a ) 287 , b ) 100 , c ) 125 , d ) 988 , e ) 271 | "3 x * 2 x = 2400 = > x = 20 2 ( 60 + 40 ) = 200 m 200 * 1 / 2 = rs . 100 answer : b" |
Solve the problem systematically, showing each step clearly. | 8 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ? a ) 144 , b ) 131 , ... | "there are 8 business exec and in each handshake 2 business execs are involved . hence 8 c 2 = 28 also , each of 8 exec will shake hand with every 7 other chairmen for total of 56 handshake . total = 28 + 56 = 84 ans : d" |
Provide a detailed solution to the given mathematical problem. | if 11 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes a ) 55 , b ) 42 , c ) 43 , d ) 44 , e ) 45 | "n ( n - 1 ) / 2 = 11 * 10 / 2 = 55 answer : a" |
Provide a detailed solution to the given mathematical problem. | what number is obtained by adding the units digits of 734 ^ 98 and 347 ^ 82 ? a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15 | "the units digit of 734 ^ 98 is 6 because 4 raised to the power of an even integer ends in 6 . the units digit of 347 ^ 82 is 9 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 82 is in the form 4 n + 2 , the units digit is 9 . then 6 + 9 = 15 . the answer is e ." |
Work through the equation methodically, ensuring clarity at each step. | the average of 10 numbers is calculated as 46 . it is discovered later on that while calculating the average , the number 75 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ? a ) 48 , b ) 51 , c ) 60 , d ) 71 , e ) 96 | "the total sum of the numbers should be increased by 50 . then the average will increase by 50 / 10 = 5 . the correct average is 51 . the answer is b ." |
Solve the problem systematically, showing each step clearly. | there are 100 students in a certain geometry class . if one half of the students are boys and one fifth of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ? a ) 6 , b ) 10 , c ) 18 , d ) 24 , e ) 27 | total students = 100 one half of the students are boys = 1 / 2 * 100 = 50 one fifth of the boys are under six feet tall = 1 / 5 * 50 = 10 . . . therefore number of boys in the class under six feet tall = 10 . . . answer b . . . . alternatively . . . number of boys in the class under six feet tall = 1 / 5 of 1 / 2 of to... |
Work through the equation methodically, ensuring clarity at each step. | find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 29 | "( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 3 x 11 ^ 2 = 2 ^ 22 x 7 ^ 3 x 11 ^ 2 total number of prime factors = ( 22 + 3 + 2 ) = 27 . answer is d ." |
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