XAT 2020 — QA & DI Question 17
X, Y and Z start a web-based venture together. X invests Rs. 2.5 lakhs, Y invests Rs. 3.5 lakhs, and Z invests Rs. 4 lakhs. In the first year, the venture makes a profit of Rs. 2 lakhs. A part of the profit is shared between Y and Z in the ratio of 2 : 3, and the remaining profit is divided among X, Y and Z in the ratio of their initial investments.
The amount that Z receives is four times the amount that X receives. How much amount does Y receive?
Answer & solution
- A
Rs. 80,200
Rs. 75,000
- C
Rs. 93,750
- D
Rs. 74,250
- E
Rs. 1,02,500
Let Rs. 5P is divided between Y and Z in the ratio of 2 : 3.
∴ Y received 2P and Z received 3P.
Remaining profit = 2,00,000 – 5P
This will be dived amongst X, Y and Z in the ratio 2.5 : 3.5 : 4 = 5 : 7 : 8.
∴ X receives 5/20 × (2,00,000 – 5P) and Z receives 8/20 × (2,00,000 – 5P)
Total amount received by X = 5/20 × (2,00,000 – 5P)
Total amount received by Z = 3P + 8/20 × (2,00,000 – 5P)
According to the question:
3P + 8/20 × (2,00,000 – 5P) = 4(5/20 × (2,00,000 – 5P))
⇒ 3P + 80,000 – 2P = 2,00,000 – 5P
⇒ 6P = 1,20,000
⇒ P = 20,000
∴ Y receives = 2P + 7/20 × (2,00,000 – 5P) = 40,000 + 7/20 × 1,00,000 = 75,000
Hence, option (b).