Question

The sum of the ages of Anup and his father is 100. When Anup is as old as his father now, he will be five times as old as his son Anuj is now. Anuj will be eight years older than Anup is now, when Anup is as old as What are their ages now?

Answer 1

Given:-

• The sum of ages if Anup and his father = 100.
• Anup is five times older than his son Anuj now.
• Anuj will be eight years older than Anup is now.

To Find:-

• What are their ages now =?

Solution:-

Let Anup age be x and Anup 's father age be y.

Then x + y = 100

Father's age y = 100 - x

When Anup is as old as his father , his age will be ( 100 - x) - x = (100 - 2x)

Hence, Anup will reach his father's age after (100 - 2x ) years.

Anuj's age now = $\sf\frac{1}{5}$ of Anup 's age when his age equals his father 's age = $\sf\frac{100 - x}{5}$

Anuj's age when Anup attain's his father's age that is after (100 -2x) Years = $\sf\frac{100 -x}{5}$ + (100 -2x)

This age is eight years more than Anup's age now that is 8 more than x = x + 8

Hence, $\sf\frac{100 -x}{5}$ + (100 -2x) = x + 8

Solving,

• Anup's age x = 35
• Anup's father's age = 65
• Anuj's Age = $\sf\frac{100-35}{5}$ = 13.