# A mother and her two daughters got a room constructed for ₹ 62,000.

Question:

A mother and her two daughters got a room constructed for ₹ 62,000. The elder daughter contributes 3/8 of her mother’s contribution while the younger daughter contributes ½ of her mother’s share. How much do the three contribute individually?

Solution:

From the question it is given that,

A mother and her two daughters got a room constructed for = ₹ 62,000

Let us assume mother’s share be x,

Then,

The elder daughter’s contribute = 3/8 of her mother’s share

= 3/8 x

The younger daughter’s contribute = ½ of her mother’s share

= ½ x

So, mother’s share + elder daughter’s share + younger daughter’s share = ₹ 62,000

x + (3/8) x + ½ x = ₹ 62,000

The LCM of the denominators 1, 8 and 2 is 8

(1/1) = [(1×8)/ (1×8)] = (8/8)

(3/8) = [(3×1)/ (8×1)] = (3/8)

(1/2) = [(1×4)/ (2×4)] = (4/8)

Then,

(8/8) x + (3/8) x + (4/8) x = 62,000

(8x + 3x + 4x)/8 = 62,000

(15x/8) = 62,000

15x = 62,000 × 8

X = 496000/15

X = ₹ 33,066.6

∴Mother’s share = ₹ 33,066.6

Elder daughter’s share = 3/8 of her mother’s share

= 3/8 x

= 3/8 × 33066.6

= ₹ 12,400

Younger daughter’s share = ½ of her mother’s share

= ½ x

= ½ × 33066.6

= ₹ 16,533.3