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Present Age Ratio

Introduction

In aptitude tests, age ratio problems are very common. Instead of giving the exact difference in ages, the question provides the ratio of present ages. With this, we can form simple equations and solve them step by step.

These problems may look tricky at first, but if you follow a clear process, they become very easy. Let’s learn the logic and solve an example together.

Pattern: Present Age Ratio

Pattern

The key idea in ratio-based age problems is:

If the ratio of A’s age to B’s age is x : y, then we can write it as:
A = xk, B = yk (where k is a common multiplier)

This multiplier k represents the actual scale of the ratio. Once we find it using the given condition, we can calculate both ages.

Step-by-Step Example

Question

The ratio of Rahul’s age to Neha’s age is 3 : 2. The difference between their ages is 10 years. Find their present ages.

Options:

  1. Rahul 28, Neha 18
  2. Rahul 30, Neha 20
  3. Rahul 32, Neha 22
  4. Rahul 27, Neha 17

Solution

  1. Step 1: Represent the ratio with a multiplier.

    “The ratio is 3 : 2” → Rahul’s age = 3k, Neha’s age = 2k.

  2. Step 2: Use the given condition.

    “The difference between their ages is 10” → (3k - 2k) = k = 10.

  3. Step 3: Find their actual ages.

    Rahul’s age = 3k = 3 × 10 = 30
    Neha’s age = 2k = 2 × 10 = 20

  4. Final Answer:

    Rahul = 30, Neha = 20 → Option B

  5. Quick Check:

    Ratio = 30 : 20 = 3 : 2 ✅
    Difference = 30 - 20 = 10 ✅

Quick Variations

If instead of the difference, the question gives the sum of ages, simply add: 3k + 2k = 5k.

For example: If the ratio is 3 : 2 and the sum is 50, then 5k = 50 → k = 10 → Ages are 30 and 20.

Trick to Always Use

  • Step 1: Express ages as ratio multiples (xk, yk).
  • Step 2: Use the given condition (difference, sum, or relation) to find k.
  • Step 3: Substitute back to get actual ages.
  • Step 4: Always verify by checking the ratio.

Summary

Summary

  • Write ages as xk and yk to convert a ratio into algebraic form.
  • Use the provided condition (difference, sum or relation) to form a simple equation and solve for k.
  • Substitute k back to get actual ages and present them clearly.
  • Always verify both the ratio and the additional condition (sum/difference) as a quick check.

Example to remember:
If ratio = 3 : 2 and difference = 10 → k = 10 → ages = 30 and 20.

Practice

(1/5)
1. The ratio of Rahul's age to Neha's age is 3 : 2. The difference between their ages is 10 years. Find their present ages.
easy
A. 30 and 20
B. 20 and 10
C. 15 and 5
D. 25 and 15

Solution

  1. Step 1: Represent the ratio with a multiplier.

    Rahul = 3k, Neha = 2k.

  2. Step 2: Use the difference.

    Difference = 3k - 2k = k = 10 → k = 10.

  3. Step 3: Find actual ages.

    Rahul = 3×10 = 30, Neha = 2×10 = 20.

  4. Final Answer:

    Rahul = 30, Neha = 20 → Option A

  5. Quick Check:

    30 : 20 = 3 : 2 ✅
Hint: Write ages as xk, yk; difference = (x-y)k gives k quickly.
Common Mistakes: Forgetting to use (x-y)k for the difference; mixing up which is larger.
2. The ratio of A to B is 5 : 4. Their total age is 45 years. Find A and B.
easy
A. 25 and 20
B. 20 and 25
C. 30 and 15
D. 15 and 30

Solution

  1. Step 1: Represent ages.

    A = 5k, B = 4k.

  2. Step 2: Use the sum.

    5k + 4k = 9k = 45 → k = 5.

  3. Step 3: Find ages.

    A = 5×5 = 25, B = 4×5 = 20.

  4. Final Answer:

    A = 25, B = 20 → Option A

  5. Quick Check:

    25 : 20 = 5 : 4 ✅
Hint: Sum the ratio parts, divide total by that to get k.
Common Mistakes: Dividing by wrong total parts or swapping A and B in final assignment.
3. Rahul’s age is 30. If the ratio Rahul : Neha is 3 : 2, what is Neha’s age?
easy
A. 15
B. 18
C. 20
D. 25

Solution

  1. Step 1: Express ages as ratio multiples.

    Rahul = 3k, Neha = 2k.

  2. Step 2: Use Rahul's actual age to find k.

    3k = 30 → k = 10.

  3. Step 3: Find Neha's age.

    Neha = 2×10 = 20.

  4. Final Answer:

    Neha = 20 → Option C

  5. Quick Check:

    30 : 20 = 3 : 2 ✅
Hint: If one actual age is given, divide by its ratio part to get k.
Common Mistakes: Using wrong ratio part for the given person (swap if needed).
4. The ratio of P to Q is 4 : 5. If their difference is 6 years, find their ages.
medium
A. 20 and 26
B. 24 and 30
C. 16 and 22
D. 12 and 18

Solution

  1. Step 1: Represent ages.

    P = 4k, Q = 5k.

  2. Step 2: Use the difference.

    5k - 4k = k = 6 → k = 6.

  3. Step 3: Find ages.

    P = 4×6 = 24, Q = 5×6 = 30.

  4. Final Answer:

    P = 24, Q = 30 → Option B

  5. Quick Check:

    30 - 24 = 6 and ratio 24:30 = 4:5 ✅
Hint: Difference = (b-a)k quickly gives k when difference is given.
Common Mistakes: Mixing up which is larger; use larger ratio part for the older person.
5. The ratio of X to Y is 7 : 3 and their total age is 40 years. Find X and Y.
medium
A. 28 and 12
B. 21 and 19
C. 30 and 10
D. 35 and 5

Solution

  1. Step 1: Represent ages.

    X = 7k, Y = 3k.

  2. Step 2: Use the sum.

    7k + 3k = 10k = 40 → k = 4.

  3. Step 3: Find ages.

    X = 7×4 = 28, Y = 3×4 = 12.

  4. Final Answer:

    X = 28, Y = 12 → Option A

  5. Quick Check:

    28 + 12 = 40 and ratio 28:12 = 7:3 ✅
Hint: Total ÷ sum_of_parts = k, then multiply each ratio part by k.
Common Mistakes: Forgetting to multiply both parts by the same k; mixing sum with difference formulas.

Mock Test

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