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Conditional Statements in Age

Introduction

Some age problems give information using conditions rather than direct ages. For example: "Rahul is twice as old as Neha" or "After 5 years, father will be 3 times the son’s age". These are called Conditional Statement age problems.

The key is to assign variables to unknown ages and convert each sentence into a clear equation. Once you do this, solving becomes straightforward.

Pattern: Conditional Statements in Age

Pattern

The key idea:

Assign a variable to the unknown age (usually the youngest person).

Translate each sentence of the problem into a mathematical equation using the given condition.

Solve the resulting equation(s) to find the required age(s).

Step-by-Step Example

Question

Rahul is twice as old as Neha. After 5 years, he will be 3 years older than Neha. Find their present ages.

Options:

  • A: Neha = 3 years, Rahul = 6 years
  • B: Neha = 4 years, Rahul = 8 years
  • C: Neha = 5 years, Rahul = 10 years
  • D: Neha = 6 years, Rahul = 12 years

Solution

  1. Step 1: Assign variables.

    Let Neha’s present age = x.
    Rahul’s present age = 2x (twice Neha).

  2. Step 2: Translate the future condition.

    After 5 years:
    Neha = x + 5
    Rahul = 2x + 5
    Condition: 2x + 5 = (x + 5) + 3

  3. Step 3: Solve the equation.

    2x + 5 = x + 8
    x = 3

  4. Step 4: Find actual ages.

    Neha = 3 years
    Rahul = 6 years

  5. Final Answer:

    Neha = 3 years, Rahul = 6 years → Option A

  6. Quick Check:

    After 5 years: Neha = 8, Rahul = 11 → difference = 3 years ✅

Quick Variations

Conditional statements can involve past ages, future ages, or multiples of ages. The process is always: assign variable → translate condition → solve equation.

Trick to Always Use

  • Step 1: Assign variable to the unknown age.
  • Step 2: Convert each condition into an equation.
  • Step 3: Solve carefully.
  • Step 4: Verify using the original condition.

Summary

Summary

  • Identify the unknown(s) and assign variables.
  • Translate conditional statements into equations accurately.
  • Solve step-by-step to get the required ages.
  • Verify by plugging values back into the condition.

Example to remember: Assign variable → Translate → Solve → Verify

Practice

(1/5)
1. If X is older than Y and their total is 30, and Y is 10, find X’s age.
easy
A. 18
B. 20
C. 22
D. 25

Solution

  1. Step 1: Translate the condition.

    X + Y = 30 and Y = 10.

  2. Step 2: Solve for X.

    X = 30 - 10 = 20.

  3. Final Answer:

    20 → Option B

  4. Quick Check:

    20 + 10 = 30 ✅
Hint: Subtract the known age from the total.
Common Mistakes: Adding instead of subtracting.
2. If A is twice B and their total is 36, find A and B.
easy
A. 24 and 12
B. 20 and 16
C. 18 and 18
D. 28 and 8

Solution

  1. Step 1: Translate the condition.

    A = 2B and A + B = 36.

  2. Step 2: Substitute and solve.

    2B + B = 36 → 3B = 36 → B = 12.

  3. Step 3: Find A.

    A = 2 × 12 = 24.

  4. Final Answer:

    A = 24, B = 12 → Option A

  5. Quick Check:

    24 + 12 = 36 ✅
Hint: Replace A with 2B in the total equation.
Common Mistakes: Forgetting to substitute correctly before solving.
3. If P is 5 years older than Q and the sum is 35, find P and Q.
medium
A. 20 and 15
B. 18 and 17
C. 22 and 13
D. 25 and 10

Solution

  1. Step 1: Write equations.

    P = Q + 5 and P + Q = 35.

  2. Step 2: Substitute and solve.

    (Q + 5) + Q = 35 → 2Q + 5 = 35 → Q = 15.

  3. Step 3: Find P.

    P = 15 + 5 = 20.

  4. Final Answer:

    P = 20, Q = 15 → Option A

  5. Quick Check:

    20 + 15 = 35 ✅
Hint: Express older person as younger + difference.
Common Mistakes: Using P = Q - 5 instead of Q + 5.
4. If a father is 3 times his son and their sum is 48, find their ages.
medium
A. 36 and 12
B. 30 and 18
C. 34 and 14
D. 40 and 8

Solution

  1. Step 1: Translate the condition.

    F = 3S and F + S = 48.

  2. Step 2: Substitute and solve.

    3S + S = 48 → 4S = 48 → S = 12.

  3. Step 3: Find father’s age.

    F = 3 × 12 = 36.

  4. Final Answer:

    Father = 36, Son = 12 → Option A

  5. Quick Check:

    36 + 12 = 48 ✅
Hint: Let the younger person be the variable when the elder is a multiple.
Common Mistakes: Wrong assumption like F = S/3 instead of F = 3S.
5. If A is 4 times B and B is 6 years old, find A’s age.
medium
A. 20
B. 22
C. 24
D. 26

Solution

  1. Step 1: Translate the relationship.

    A = 4B, B = 6.

  2. Step 2: Solve for A.

    A = 4 × 6 = 24.

  3. Final Answer:

    24 → Option C

  4. Quick Check:

    24 ÷ 6 = 4 ✅
Hint: Multiply when direct multiple relation is given.
Common Mistakes: Dividing instead of multiplying.

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