Question

The sum of ages of anup and his father is 100.When anup is as old as his father now, he will be 5 times as old as anuj is now. Anuj will be 8 years older than anup is now, when anup is is as old as his father. What are their ages?

Answer 1

Answer:

Step-by-step explanation:

Let Anup's age be A and Anup's father's age = F. Then A + F = 100.

Father's age F = 100 - A.

When Anup is as old as his father, his age will be (100 - A).

Difference between Anup's age now and then = (100 - A) - A = (100 - 2A).

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

Anuj's age now = (1/5) of Anup's age when his age equals his father's age                       = (100 - A)/5.

Anuj's age when Anup attains his father's age,i.e., after (100 - 2A) Years = [(100 - A)/5] + (100 - 2A).

This age is 8 years more than Anup's age now,i.e., 8 more than A = A + 8.

Hence [(100 - A)/5] + (100 - 2A) = A + 8

Solving, Anup's age A = 35, Anup's father's age F = 65, Anuj's age = (100 - 35)/5 = 13. 

Answer 2

Step-by-step explanation:

let the age of Anup be x years then anup's father's age will be 100-x years

now, when Anup becomes his father's age that means when Anup' s age will 100-x years.

so after 100-x -x = 100-2x years Anup will become his father's age.

now a/q = when Anup ' s age is 100-x years then he will 5 times as old as his son Anuj means anuj's present age = 100-x/5 years

but after 100-2x years Anuj 's age will become (100-x/5 + 100-2x) years

an at the same time, Anuj's age is 8 years older than present age of Anup 's age

= 100-x/5 + 100 - 2x = x + 8

= 100-x + 5( 100- 2x)/5 = x+8

= 100-x + 500 - 10x / 5 = x + 8

= 600 - 11x = 5(x + 8)

= 600 - 11x = 5x + 40

= 560 = 16x = -16x = -560

= 16x = 560

= x = 35

so, anup's present age = x = 35 years

and anup's father's age = 100-x = 100-35 = 65 years

and Anuj's present age = 100-x/5 = 100-35/5 = 65/5 = 13 years