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Age Sum Given

Introduction

In some aptitude problems, instead of giving the difference or ratio, the question provides the sum of present ages. Using this information along with an additional condition, we can form equations and find the actual ages.

These problems look straightforward if you carefully translate the conditions into equations. Let’s understand the pattern with a clear example.

Pattern: Age Sum Given

Pattern

The key idea:

If the sum of A’s and B’s ages is given, we can write:
A + B = (given value)

Then, use the second condition (ratio, difference, or relation) to split the sum into actual ages.

Step-by-Step Example

Question

The sum of Rahul’s and Neha’s present ages is 50 years. If Rahul is 4 years older than Neha, find their present ages.

Options:

  • A: Rahul 27, Neha 23
  • B: Rahul 26, Neha 24
  • C: Rahul 28, Neha 22
  • D: Rahul 25, Neha 25

Solution

  1. Step 1: Represent the ages.

    “Rahul is 4 years older than Neha” → Let Neha’s present age = N, Rahul’s present age = N + 4.

  2. Step 2: Use the sum condition.

    “The sum of their ages is 50” → N + (N + 4) = 50 → 2N + 4 = 50

  3. Step 3: Solve the equation.

    2N + 4 = 50 → 2N = 46 → N = 23

  4. Step 4: Find Rahul’s age.

    Rahul = N + 4 = 23 + 4 = 27

  5. Final Answer:

    Rahul = 27, Neha = 23 → Option A

  6. Quick Check:

    23 + 27 = 50 ✅

Quick Variations

If instead of the difference, the second condition gives a ratio (e.g., “Their ages are in the ratio 3:2”), then split the sum accordingly.

Example: Sum = 50, ratio = 3:2 → (3+2) parts = 5 parts = 50 → 1 part = 10 → Ages = 30 and 20.

Trick to Always Use

  • Step 1: Represent the ages using variables.
  • Step 2: Apply the given sum condition.
  • Step 3: Use the second condition (difference/ratio) to split the sum.
  • Step 4: Solve and verify.

Summary

Summary

The Age Sum Given pattern is solved by combining the sum condition with an extra condition like difference or ratio.

  • Step 1: Write A + B = (given sum).
  • Step 2: Use the extra condition to form a second equation.
  • Step 3: Solve for actual ages.
  • Step 4: Double-check by adding again.

Once you master this, sum-based age problems will be quick and easy to solve!

Practice

(1/5)
1. The sum of Rahul's and Neha's ages is 50 years. If Rahul is 30 years old, what is Neha's age?
easy
A. 20
B. 30
C. 25
D. 15

Solution

  1. Step 1: Translate the sentence.

    The sum of Rahul and Neha = 50; Rahul = 30.

  2. Step 2: Use the sum to find Neha.

    Neha = 50 - 30 = 20.

  3. Final Answer:

    20 → Option A

  4. Quick Check:

    30 + 20 = 50 ✅
Hint: Subtract the known age from the total to get the other age.
Common Mistakes: Swapping ages or subtracting in the wrong order.
2. The total age of 3 sisters is 48 years. Two of them are 14 and 15 years old. What is the age of the third sister?
easy
A. 20
B. 19
C. 21
D. 18

Solution

  1. Step 1: Translate the sentence.

    Total of three sisters = 48; two ages = 14 and 15.

  2. Step 2: Subtract known ages from the total.

    Third = 48 - (14 + 15) = 48 - 29 = 19.

  3. Final Answer:

    19 → Option B

  4. Quick Check:

    14 + 15 + 19 = 48 ✅
Hint: Add the known ages first, then subtract from the total.
Common Mistakes: Forgetting to add the known ages correctly before subtracting.
3. Four friends have a total age of 80 years. Three are 18, 21 and 17. Find the fourth friend's age.
easy
A. 22
B. 25
C. 24
D. 20

Solution

  1. Step 1: Translate the sentence.

    Total of 4 friends = 80; three ages = 18, 21, 17.

  2. Step 2: Sum known ages and subtract.

    Sum known = 18 + 21 + 17 = 56. Fourth = 80 - 56 = 24.

  3. Final Answer:

    24 → Option C

  4. Quick Check:

    18 + 21 + 17 + 24 = 80 ✅
Hint: Group additions first, then subtract from total to minimize errors.
Common Mistakes: Arithmetic errors when adding several ages.
4. The sum of ages of A and B is 50 years. A is 4 years older than B. Find their present ages.
medium
A. A 26, B 24
B. A 28, B 22
C. A 29, B 21
D. A 27, B 23

Solution

  1. Step 1: Translate to equations.

    A + B = 50 and A = B + 4.

  2. Step 2: Substitute and solve.

    (B + 4) + B = 50 → 2B + 4 = 50 → 2B = 46 → B = 23. Then A = 23 + 4 = 27.

  3. Final Answer:

    A = 27, B = 23 → Option D

  4. Quick Check:

    27 + 23 = 50 and difference = 4 ✅
Hint: Express older as younger + gap, substitute into the sum, solve for younger.
Common Mistakes: Confusing which person is older when setting equations.
5. The combined age of a father and son is 50 years. Father is 30 years older than son. Find their present ages.
medium
A. Father 40, Son 10
B. Father 41, Son 9
C. Father 42, Son 8
D. Father 45, Son 5

Solution

  1. Step 1: Translate to equations.

    Father + Son = 50 and Father = Son + 30.

  2. Step 2: Substitute and solve.

    (Son + 30) + Son = 50 → 2×Son + 30 = 50 → 2×Son = 20 → Son = 10. Father = 10 + 30 = 40.

  3. Final Answer:

    Father = 40, Son = 10 → Option A

  4. Quick Check:

    40 + 10 = 50 and father - son = 30 ✅
Hint: Use substitution for elder = younger + gap, then solve using the sum.
Common Mistakes: Using wrong gap sign or mixing up ages when substituting.

Mock Test

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