Multiple choice

The sum of the present ages of two persons is seven times that of the difference between their ages. After 5 years, the sum of their ages will become nine times that of the difference. What is the present age of the elder person?

  1. 24 years

  2. 28 years

  3. 14 years

  4. 20 years

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let ages be x (elder) and y. Given: x+y=7(x-y) and (x+5)+(y+5)=9(x-y). Simplify first: x+y=7x-7y → 8y=6x → x=4y/3. Second: x+y+10=9x-9y → 10y+10=8x → substitute x: 10y+10=8(4y/3) → 30y+30=32y → y=15, x=20. Elder is 20.