Question

Present age of mother of Manish is 1 year more than 5 times the present age of Manish. Four years before, if the product of their ages was 22, then find the present age of Manish and his mother

Answer 1

Let the present age of Manish be x years.

The present age of the mother of Manish is 1 year more than 5 times the present age of Manish.

∴ The present age of the mother of Manish will be (5x + 1) years.

Four years before,

Manish’s age was (x – 4) years and

Mother’s age was (5x + 1 – 4) years i.e., (5x – 3) years

According to the given condition,

Four years before, the product of their ages was 22.

∴ (x – 4)(5x – 3) = 22

∴ 5x² – 3x – 20x + 12 – 22 = 0

∴ 5x² – 23x – 10 = 0

5 × (-10) =	-50
	+25  +2
	(-25) × 2 = -50
	-25 + 2 = -23

∴ 5x² – 25x + 2x – 10 = 0

∴ 5x(x – 5) + 2(x – 5) = 0

∴ (x – 5)(5x + 2) = 0

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get

x – 5 = 0 or 5x + 2 = 0

∴ x = 5 or x = `(-2)/5`

But, age cannot be negative.

∴ x = 5

∴ Manish’s present age = x = 5 years,

Mother’s present age = 5x + 1

= 5(5) + 1

= 25 + 1

= 26 years