Three people named 'W', 'X' and 'Y' together start a business by investing Rs. 4a, Rs. 20,000, and Rs. 5b, respectively. 'W' invested his amount for 10 months, 'X' and 'Y' invested their amount for 2 more months than 'W'. One year after starting the business, the sum of profit shares of 'X' and 'Y' was 35% more than that of 'W' and the share of 'X' was 80% of that of 'Y'. Find the sum of the initial investment of 'W' and 'Y'.
Show answer & explanation
Correct answer: D
Explanation
Given:
W = 4a (10 months), X = 20,000 (12 months), Y = 5b (12 months)
X's share = 80% of Y's share
X + Y = 35% more than W
W = 4a × 10 = 40a
X = 20,000 × 12 = 240,000
Y = 5b × 12 = 60b
X : Y = 80 : 100 = 4 : 5
⇒ 240,000 : 60b = 4 : 5
⇒ 240,000 × 5 = 4 × 60b
⇒ 1,200,000 = 240b
⇒ b = 5,000
Y = 5b = 25,000
Now,
X + Y = 240,000 + 300,000 = 540,000
Given:
X + Y = 1.35 W
540,000 = 1.35 × 40a
540,000 = 54a
a = 10,000
W = 4a = 40,000
W + Y = 40,000 + 25,000 = 65,000 Rupees