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 his father.what are their ages right now. ​

Answer 1

Solution :

• The sum of the ages of Anup and his father is 100 years

• When Anup is as old as his father now, he will be five times as old as Anuj (now).

• Anuj will be 8 years older than current age of Anup , when Anup is as old as his father .

The shortest method to solve this is to take the only variable as the of Anup .

Let us assume that the age of Anup is x years .

The age of his father is (100-x) years. [ Statement 1]

Time taken by Anup to reach age of his father : (100 - 2x) years.

Current age of Anuj = ⅕( 100 - x). [ Statement 2]

(100-2x) + ⅕( 100 - x) = x + 8. [ Statement 3]

> 100 - 2x + 20 - ⅕x = x + 8

> x + 2x + ⅕x = 120 - 8

> 3x + ⅕x = 112

> 16/5 x = 112

x = (112/16) × 5

> x = 35 years

100-x = 65 years

( 100 - x)/5 = 13 years

Answer :

Age of Anup is 35 years .

Age of Anuj is 13 years.

Age of their father is 65 years.

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Answer 2

Given :-

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 his father.

To Find :-

Present ages

Solution :-

Let the age of Anup be x

Age of father = 100 - x

Now

ATQ

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

100 - 2x + 20 - x/5 = x + 8

120 - 3x/5 = x + 8

120 - 8 = 3x + x/5

112 = 15x + x/5

112 = 16x/5

112(5) = 16x

560/16 = x

35 = x

Now

Age of Anuj = 35 years

Age of father = 100 - 35 = 65 years

Age of Anup = 100 - 35/5 = 65/5 = 13 years