The age of father is twice that the sum of ages of his two sons. 20 years later, the age of father will become the sum of ages of his two sons. The present age of father is

Let the father's present age be F and the sum of the two sons' present ages be S. The first statement gives F = 2S.

Twenty years later the father is F + 20. Each of the two sons has aged 20 years, so the sum of their ages rises by 40 and becomes S + 40. The second statement gives F + 20 = S + 40, so F = S + 20.

Solving 2S = S + 20 gives S = 20 and F = 40. Check: father 40, sons' sum 20; after 20 years, father 60, sons' sum 60. It fits.

• B (60): sons' sum 30, so 80 vs 70 after 20 years. Fails.
• C (30): sons' sum 15, so 50 vs 55. Fails.
• D (50): sons' sum 25, so 70 vs 65. Fails.

The core concept is translating age statements into simultaneous linear equations, where time shifts act differently on the father and the sum of several children. This is a standard quantitative aptitude tool that also helps in data-interpretation questions.

Trap: aspirants add 20 years to the sons' sum as well, writing F + 20 = S + 20. That wrongly gives F = S, which contradicts F = 2S. Remember that two sons each age 20 years, so the sum grows by 40.