5 years ago, the sum of my mother's and my ages was 40 years. Now the ratio of our ages is 4 : 1. What is my mother's age?

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UKPSC Lower PCS Preliminary Exam Official Paper (Held On: 11 May, 2025)
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  1. 32 years
  2. 40 years
  3. 60 years
  4. 26 years

Answer (Detailed Solution Below)

Option 2 : 40 years
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Detailed Solution

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Given:

5 years ago, the sum of my mother's and my ages = 40 years.

Now, the ratio of our ages = 4 : 1.

Calculation

Let my age 5 years ago = x years, and my mother's age 5 years ago = y years.

1. x + y = 40

2. Current ages ratio: (y + 5) / (x + 5) = 4 / 1

From equation 1:

y = 40 - x

Substitute y in equation 2:

(40 - x + 5) / (x + 5) = 4 / 1

⇒ (45 - x) / (x + 5) = 4

⇒ 45 - x = 4 × (x + 5)

⇒ 45 - x = 4x + 20

⇒ 45 - 20 = 4x + x

⇒ 25 = 5x

⇒ x = 25 / 5

⇒ x = 5

Now, y = 40 - x

⇒ y = 40 - 5

⇒ y = 35

Current age of my mother = y + 5

⇒ 35 + 5 = 40

My mother's current age is 40 years.

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