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Linear equations · 3 marks

The present age of Salil’s mother is three times Salil’s present age. After 5 years, their ages will add up to 70 years. Find their present ages.

Answer: Salil is 15 years old and his mother is 45 years old.

Step-by-step solution

Given: Mother’s present age = 3 × Salil’s present age; After 5 years, the sum of their ages = 70 years
To find: Their present ages

Idea: Let Salil’s age be x. After 5 years both are 5 years older, so add 5 to each age before adding them.

  1. Let Salil’s present age be x years. Then his mother’s present age is 3x years.½ mark
  2. After 5 years: Salil is x + 5 and his mother is 3x + 5.½ mark
  3. (x + 5) + (3x + 5) = 70, so 4x + 10 = 70.1 mark
  4. 4x = 60, so x = 15. Mother’s age = 3 × 15 = 45.½ mark
  5. Salil is 15 years old and his mother is 45 years old.½ mark
Salil’s present age is 15 years and his mother’s present age is 45 years.

Check: 45 = 3 × 15 ✓. In 5 years: 20 + 50 = 70 ✓.

Answer to write in the exam

Let Salil’s present age = x years; mother’s present age = 3x years

After 5 years: (x + 5) + (3x + 5) = 70

4x + 10 = 70 ⇒ 4x = 60 ⇒ x = 15

Mother’s age = 3 × 15 = 45

∴ Salil is 15 years old and his mother is 45 years old

Common mistakes that cost marks

  • Adding 5 only once: x + 3x + 5 = 70. Both people get 5 years older, so the sum grows by 10.
  • Giving the ages after 5 years (20 and 50) instead of the present ages.
  • Writing the mother’s age as x + 3 instead of 3x (“three times” means multiply).

How this can come in the exam

MCQ (1 mark)

A father is 4 times as old as his son. In 6 years the sum of their ages will be 62. The son’s present age is

  1. 10 years
  2. 12 years
  3. 8 years
  4. 14 years
Show answer

(A) 10 years
x + 6 + 4x + 6 = 62, so 5x = 50 and x = 10.

Short answer (3 marks)

Anu’s mother is 26 years older than Anu. Three years ago, the sum of their ages was 46 years. Find their present ages.

Show answerPresent ages a and a + 26 (1 mark). Three years ago: (a − 3) + (a + 23) = 46, so 2a + 20 = 46 (1 mark). a = 13: Anu 13, mother 39 (1 mark).

Try one yourself

Ravi’s grandfather is 5 times Ravi’s age. After 4 years, their ages will add up to 80. Find their present ages.

Show answer

x + 4 + 5x + 4 = 80, so 6x = 72 and x = 12. Ravi is 12 and his grandfather is 60.

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