Question

Present ages of Anu and Raj are in the ratio 4:5. Eight years from now the ratio of their ages will be 5:6. Find their present ages.

(a) Raj’s age is 32 years and Anu’s age is 40 years

(b) Raj’s age is 40 years and Anu’s age is 48 years

(c) Raj’s age is 32 years and Anu’s age is 32 years

(d) Raj’s age is 40 years and Anu’s age is 32 years

I got this question at a job interview.

Enquiry is from Age/Money/Denomination of Currency Word Problems topic in section Linear Equations in One Variable of Mathematics – Class 8

Answer 1

Correct option is (d) Raj’s age is 40 years and Anu’s age is 32 years

The explanation: Let the present ages of Anu and Raj be 4x years and 5x years respectively.

After eight years. Anu’s age = (4x + 8) years;

After eight years, Raj’s age = (5x + 8) years.

∴ the ratio of their ages after eight years = \(\frac{4x+8}{5x+8}\)

This is given to be 5:6.

∴ \(\frac{4x+8}{5x+8} = \frac{5}{6}\)

∴ 6(4x+8)=5(5x+8)

∴ 24x+48=25x+40

∴ –x=-8

∴ x=8

∴ Anu’s age = 4×8 = 32years

∴ Raj’s age = 5×8 = 40years.