# Problems on Ages

Q31. One year ago, Ram was 8 times as old as his son. Now his age is equal to the square of his son's age. The present age of Ram will be.

(a) 40 years

(b) 42 years

(c) 45 years

(d) 49 years

**Answer:** (d) 49 years

Let, the present age of Son's be x years

∴ the present age of Ram's be 8 (x - 1) + 1 = 8x - 7

A/Q 8x - 7 = x^{2}

⇒ x^{2} - 8x + 7 = 0

⇒ x^{2} - 7x - x + 7 = 0

⇒ x(x - 7) - 1(x - 7) = 0

⇒ (x - 7) (x - 1) = 0

∴ x = 7 , x = 1

∴ Ram's present age = 8 X 7 - 7 = 56 - 7 = 49 years

Q32. Kamala got married 6 years ago. Today her age is 1¼ times her age at the time of marriage. Her son's age is ^{1}/_{15} times her age. Her son's age is

(a) 2 years

(b) 3 years

(c) 4 years

(d) 5 years

**Answer:** (a) 2 years

Let, 6 years ago Kamala's age be x years

∴ Kamala's present age = x + 6 years

A/Q x + 6 = 1¼ x

⇒ x + 6 = ^{5x}/_{4}

⇒ 4x + 24 = 5x

⇒ x = 24

∴ Kamala's present age = 24 + 6 = 30 years

∴ Son's present age = 30 X ^{1}/_{15} = 2 years

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