Question

Shaad and Noor are brother and sister and having a age difference of 20 years. 4 years before their ages are in the ratio 2 ∶ 1. Find the present ages of Shaad and Noor.
1. 44, 24 years
2. 30, 10 years
3. 32, 20 years
4. 40, 20 years

Answer 1

Correct Answer - Option 1 : 44, 24 years

Given∶

Age difference between Shaad and Noor is of 20 years.

Ratio of their ages before 4 years = 2 ∶ 1

Formula Used∶

If a ∶ b = c ∶ d

Then product of Extremes = Product of means

⇒ a × d = b × c

Calculation∶

Let Shaad’s present age be ‘x’ years and Noor’s age be ‘y’ years.

So, x – y = 20      ----(1)

4 years before,

Shaad’s age was (x – 4) years

Noor’s age was (y – 4) years

According to question,

(x -4) ∶ (y – 4) years = 2 ∶ 1

⇒ x – 4 = 2y – 8

⇒ x – 2y = -4       ----(2)

Subtracting eq (1) from (2), we get,

y = 24

Put y = 24 in eq (1)

x – y = 20

⇒ x – 24 = 20

⇒ x = 24 + 20 = 44

∴ Shaad’s present age is 44 years and Noor’s present age is 24 years.