Question

Abhi and Messi are two friends. Abhi is older than Messi. If from twice the age of Abhi, 16 is subtracted, it becomes the half of the age of Messi. If from the half of the age of Abhi, 1 is subtracted, the result is still half the age of Messi. Find the present ages of Abhi and Messi.
1. 11, 9
2. 10, 8
3. 14, 12
4. 12, 10

Answer 1

Correct Answer - Option 2 : 10, 8

Given∶

Twice the age of Abhi – 16 = half of the age of Messi

Half the age of Abhi – 1 = half the age of Messi

Formula Used∶

Concept of Quadratic Equations, Factorization (Splitting the middle term method)

Calculation∶

Let Abhi’s present age be ‘x’ years and Messi’s present age is ‘y’ years.

According to the question,

2x – 16 = 1/2 y

⇒ 4x – y = 32     ----(1)

Also, 1/2 x – 1 = 1/2 y

⇒ x – y = 2      ----(2)

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

3x = 30

⇒ x = 10

Put x = 10 in eq. (2)

x – y = 2

⇒ 10 – y = 2

⇒ y = 8

∴ Abhi’s present age is 10 years and Messi’s present age is 8 years.