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id: string;
title: string;
description: string;
howToSolve: {
steps: string[];
formulas: string[];
example: {
question: string;
solution: string;
};
};
}
export interface AptitudeSubGroup {
id: string;
title: string;
icon: string;
chapters: AptitudeChapter[];
}
export interface AptitudeGroup {
id: string;
title: string;
icon: string;
subGroups?: AptitudeSubGroup[];
chapters?: AptitudeChapter[];
}
export const aptitudeData: AptitudeGroup[] = [
{
id: 'quant',
title: 'Quantitative Aptitude',
icon: '🔢',
subGroups: [
{
id: 'arithmetic',
title: 'Arithmetic',
icon: '🧮',
chapters: [
{
id: 'percentage',
title: 'Percentage',
description: 'Learn how to calculate percentages, percentage increase/decrease, and its applications.',
howToSolve: {
steps: [
"Understand the basic concept: Percentage means 'per hundred'.",
"To convert a fraction to a percentage, multiply by 100.",
"To find x% of y, use the formula: (x/100) * y.",
"For percentage change: ((New Value - Old Value) / Old Value) * 100."
],
formulas: [
"Percentage = (Part / Whole) * 100",
"Percentage Increase = (Increase / Original Value) * 100",
"x% of y = (x * y) / 100"
],
example: {
question: "If a student scores 450 out of 600, what is the percentage?",
solution: "Percentage = (450 / 600) * 100 = 0.75 * 100 = 75%."
}
}
},
{
id: 'profit-loss',
title: 'Profit & Loss',
description: 'Master the concepts of Cost Price, Selling Price, Profit, and Loss.',
howToSolve: {
steps: [
"Identify Cost Price (CP) and Selling Price (SP).",
"If SP > CP, it's a Profit. Profit = SP - CP.",
"If CP > SP, it's a Loss. Loss = CP - SP.",
"Calculate percentage using CP as the base."
],
formulas: [
"Profit % = (Profit / CP) * 100",
"Loss % = (Loss / CP) * 100",
"SP = CP * (100 + Profit%) / 100"
],
example: {
question: "An item bought for $200 is sold for $250. Find the profit percentage.",
solution: "Profit = 250 - 200 = 50. Profit % = (50 / 200) * 100 = 25%."
}
}
},
{
id: 'interest',
title: 'Simple & Compound Interest',
description: 'Calculate interest earned or paid over time.',
howToSolve: {
steps: [
"Identify Principal (P), Rate (R), and Time (T).",
"For Simple Interest, use the direct formula.",
"For Compound Interest, calculate amount first then subtract principal.",
"Ensure time is in years and rate is per annum."
],
formulas: [
"SI = (P * R * T) / 100",
"CI Amount = P(1 + R/100)^T",
"CI = Amount - P"
],
example: {
question: "Find SI on $1000 at 5% for 2 years.",
solution: "SI = (1000 * 5 * 2) / 100 = 100."
}
}
},
{
id: 'ratio',
title: 'Ratio & Proportion',
description: 'Compare quantities and solve proportional relationships.',
howToSolve: {
steps: [
"Express the ratio in its simplest form.",
"For proportions, product of extremes = product of means.",
"Divide a quantity in a given ratio by finding the value of one part.",
"Use 'x' to represent common multipliers."
],
formulas: [
"Ratio a:b = a/b",
"If a:b = c:d, then ad = bc",
"Duplicate Ratio of a:b = a²:b²"
],
example: {
question: "Divide $100 in ratio 2:3.",
solution: "Total parts = 2+3=5. 1 part = 100/5=20. Parts are 40 and 60."
}
}
},
{
id: 'average',
title: 'Average',
description: 'Calculate the central value of a set of numbers.',
howToSolve: {
steps: [
"Sum all the given values.",
"Count the total number of values.",
"Divide the sum by the count.",
"For weighted average, multiply each value by its weight before summing."
],
formulas: [
"Average = Sum of observations / Number of observations",
"Sum = Average * Count",
"Average of first 'n' natural numbers = (n+1)/2"
],
example: {
question: "Average of 10, 20, 30?",
solution: "Sum = 60. Count = 3. Average = 60/3 = 20."
}
}
},
{
id: 'mixtures',
title: 'Mixtures & Allegations',
description: 'Solve problems involving mixing of two or more ingredients.',
howToSolve: {
steps: [
"Identify the cost/concentration of two ingredients.",
"Identify the mean price/concentration of the mixture.",
"Use the allegation rule to find the ratio of mixing.",
"Apply the ratio to find specific quantities."
],
formulas: [
"Ratio (Cheaper/Dearer) = (Dearer Price - Mean Price) / (Mean Price - Cheaper Price)",
"Quantity of Cheaper / Quantity of Dearer = (d - m) / (m - c)"
],
example: {
question: "Mix rice at $20/kg and $30/kg to get $24/kg mixture. Find ratio.",
solution: "Ratio = (30 - 24) / (24 - 20) = 6 / 4 = 3:2."
}
}
},
{
id: 'tsd',
title: 'Time, Speed & Distance',
description: 'Understand the relationship between speed, time, and distance covered.',
howToSolve: {
steps: [
"Identify the two known variables among Distance, Speed, and Time.",
"Ensure units are consistent (e.g., km/hr or m/s).",
"Use the basic formula to find the third variable.",
"For relative speed, add speeds if opposite directions, subtract if same."
],
formulas: [
"Distance = Speed * Time",
"Speed = Distance / Time",
"1 km/hr = 5/18 m/s",
"Average Speed = Total Distance / Total Time"
],
example: {
question: "A car travels 150km in 3 hours. Find its speed.",
solution: "Speed = 150 / 3 = 50 km/hr."
}
}
},
{
id: 'time-work',
title: 'Time & Work',
description: 'Calculate the time taken to complete a task by individuals or groups.',
howToSolve: {
steps: [
"Find the work done by each person in one day (1/time).",
"Add their one-day work to find combined efficiency.",
"The reciprocal of combined efficiency is the total time taken.",
"For efficiency problems, use the ratio of work done."
],
formulas: [
"If A takes 'x' days, A's 1 day work = 1/x",
"Together (A+B) 1 day work = 1/x + 1/y",
"Total Time = 1 / (Combined 1 day work)"
],
example: {
question: "A takes 10 days, B takes 15 days. Together?",
solution: "1/10 + 1/15 = 5/30 = 1/6. Total time = 6 days."
}
}
},
{
id: 'pipes',
title: 'Pipes & Cisterns',
description: 'Solve problems involving filling and emptying of tanks.',
howToSolve: {
steps: [
"Treat filling pipes as positive work and leakages/emptying pipes as negative work.",
"Find the part of the tank filled/emptied in one hour.",
"Calculate net work done in one hour.",
"The reciprocal of net work is the total time to fill/empty the tank."
],
formulas: [
"Part filled in 1 hr = 1 / (Time to fill)",
"Net work = (1/fill_time) - (1/empty_time)",
"If net work is positive, tank fills. If negative, it empties."
],
example: {
question: "Pipe A fills in 4h, Pipe B empties in 6h. Time to fill if both open?",
solution: "Net work = 1/4 - 1/6 = (3-2)/12 = 1/12. Time = 12 hours."
}
}
}
]
},
{
id: 'algebra-geom',
title: 'Algebra & Geometry',
icon: '📐',
chapters: [
{
id: 'algebra',
title: 'Algebra',
description: 'Linear equations, quadratic equations, and inequalities.',
howToSolve: {
steps: [
"Isolate the variable on one side of the equation.",
"For quadratic equations, use the quadratic formula or factoring.",
"Check for extraneous solutions in radical equations.",
"Follow BODMAS/PEMDAS for simplification."
],
formulas: [
"Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a",
"(a + b)² = a² + 2ab + b²",
"(a - b)² = a² - 2ab + b²"
],
example: {
question: "Solve for x: 2x + 5 = 15",
solution: "2x = 15 - 5 => 2x = 10 => x = 5."
}
}
},
{
id: 'geometry',
title: 'Geometry',
description: 'Area, perimeter, volume, and surface area of various shapes.',
howToSolve: {
steps: [
"Identify the shape and the required metric (Area/Perimeter).",
"Ensure all units are consistent (e.g., all in cm).",
"Apply the specific formula for the shape.",
"For complex shapes, break them down into simpler ones."
],
formulas: [
"Area of Circle = πr²",
"Area of Triangle = 1/2 * base * height",
"Volume of Cylinder = πr²h"
],
example: {
question: "Find area of a circle with radius 7cm.",
solution: "Area = (22/7) * 7 * 7 = 154 sq. cm."
}
}
}
]
}
]
},
{
id: 'logical',
title: 'Logical Reasoning',
icon: '🧠',
chapters: [
{
id: 'coding-decoding',
title: 'Coding-Decoding',
description: 'Identify patterns in letters and numbers to decode messages.',
howToSolve: {
steps: [
"Write down the alphabet with their positions (A=1, B=2... Z=26).",
"Observe the relationship between the original word and the code.",
"Check for shifts (e.g., +1, -2) or reverse positions.",
"Apply the same logic to the target word."
],
formulas: [
"Forward Position: A=1, B=2...",
"Backward Position: Z=1, Y=2...",
"Opposite Letters: A-Z, B-Y, C-X (Sum of positions = 27)"
],
example: {
question: "If CAT is coded as DBU, how is DOG coded?",
solution: "C->D (+1), A->B (+1), T->U (+1). So DOG -> EPH."
}
}
},
{
id: 'blood-relations',
title: 'Blood Relations',
description: 'Solve complex family tree problems using logical deductions.',
howToSolve: {
steps: [
"Use symbols for genders (e.g., + for Male, - for Female).",
"Draw a family tree generation by generation.",
"Use horizontal lines for siblings and vertical for parents/children.",
"Double lines for married couples."
],
formulas: [
"Paternal: Father's side",
"Maternal: Mother's side",
"Siblings: Same generation"
],
example: {
question: "Pointing to a man, a woman said, 'His mother is the only daughter of my mother.' How is the woman related to the man?",
solution: "Only daughter of woman's mother is the woman herself. So, the woman's mother is the man's mother. Woman is the Mother."
}
}
},
{
id: 'puzzles',
title: 'Puzzles',
description: 'Circular, linear, and floor-based arrangements.',
howToSolve: {
steps: [
"Read all clues and identify fixed positions first.",
"Use a diagram (Circle/Line/Grid) to represent the data.",
"Eliminate impossible scenarios based on constraints.",
"Fill in the remaining gaps logically."
],
formulas: [
"Circular: Left/Right depends on facing center or away.",
"Linear: North/South facing determines left/right.",
"Floor: Start from ground floor (1) upwards."
],
example: {
question: "A, B, C are in a row. A is to the left of B. C is to the right of B. Who is in the middle?",
solution: "Order is A - B - C. B is in the middle."
}
}
}
]
},
{
id: 'verbal',
title: 'Verbal Ability',
icon: '🗣️',
chapters: [
{
id: 'grammar',
title: 'Grammar',
description: 'Parts of speech, tenses, and error detection.',
howToSolve: {
steps: [
"Check for Subject-Verb Agreement.",
"Verify the tense consistency throughout the sentence.",
"Look for common preposition and article errors.",
"Identify the main clause and subordinate clauses."
],
formulas: [
"Singular Subject -> Singular Verb",
"Plural Subject -> Plural Verb",
"Active Voice: Subject performs action"
],
example: {
question: "Find error: Neither of the two boys are present.",
solution: "'Neither' is singular. So it should be 'is' instead of 'are'."
}
}
},
{
id: 'reading-comp',
title: 'Reading Comprehension',
description: 'Strategies for solving RC passages effectively.',
howToSolve: {
steps: [
"Skim the passage to understand the main theme.",
"Read the questions before reading the passage in detail.",
"Locate keywords from questions in the text.",
"Eliminate options that are too broad or not mentioned."
],
formulas: [
"Main Idea: Usually in 1st or last paragraph.",
"Tone: Author's attitude (Critical, Neutral, etc.)",
"Inference: What is implied but not stated."
],
example: {
question: "What is the primary purpose of the author?",
solution: "Look for the central argument or the problem being discussed."
}
}
}
]
},
{
id: 'data-suff',
title: 'Data Sufficiency',
icon: '💻',
chapters: [
{
id: 'ds-basics',
title: 'DS Basics',
description: 'Learn how to decide if the given data is enough to solve a problem.',
howToSolve: {
steps: [
"Read the question carefully to understand what is asked.",
"Check Statement 1 alone. Does it give a unique answer?",
"Check Statement 2 alone. Does it give a unique answer?",
"If neither alone works, combine both statements.",
"Choose the option based on sufficiency."
],
formulas: [
"Option A: 1 alone is sufficient",
"Option B: 2 alone is sufficient",
"Option C: Both together are sufficient",
"Option D: Neither is sufficient"
],
example: {
question: "What is x? (1) x + 2 = 5 (2) y = 10",
solution: "From (1), x=3. Sufficient. From (2), no info on x. So, (1) alone is sufficient."
}
}
}
]
},
{
id: 'advanced',
title: 'Advanced Topics',
icon: '🧮',
chapters: [
{
id: 'probability',
title: 'Probability',
description: 'Calculate the likelihood of events occurring.',
howToSolve: {
steps: [
"Find the total number of possible outcomes (Sample Space).",
"Find the number of favorable outcomes.",
"Divide favorable outcomes by total outcomes.",
"Ensure the result is between 0 and 1."
],
formulas: [
"P(E) = n(E) / n(S)",
"P(A or B) = P(A) + P(B) - P(A and B)",
"P(not E) = 1 - P(E)"
],
example: {
question: "Probability of getting a head in a coin toss?",
solution: "Favorable = 1 (Head), Total = 2 (Head, Tail). P = 1/2."
}
}
},
{
id: 'p-and-c',
title: 'Permutation & Combination',
description: 'Arrangements and selections of objects.',
howToSolve: {
steps: [
"Determine if order matters (Permutation) or not (Combination).",
"Identify total items (n) and items to be selected (r).",
"Apply the appropriate factorial formula.",
"Consider constraints like repetitions or fixed positions."
],
formulas: [
"nPr = n! / (n-r)!",
"nCr = n! / [r! * (n-r)!]",
"n! = n * (n-1) * ... * 1"
],
example: {
question: "In how many ways can 3 books be selected from 5?",
solution: "Order doesn't matter. 5C3 = 5! / (3! * 2!) = (5*4)/2 = 10."
}
}
}
]
}
];
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