Two persons P and Q enter into a business. P puts 14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P's share is 400 more than Qs share out of the total profit of 2,000, what is the capital contributed by P?
This questions was previously asked in
UPSC CSAT, Previous year (2024)
Explanation:
Let's break down the problem:
- Let Q's capital be x, so P's capital is x + 14,000.
- P invests for 8 months, Q for 10 months.
- Their profit ratios = (Capital × Time).
- P's share = (x+14,000) × 8, Q's share = x × 10.
- (x+14,000)×8 : x×10 = P:Q
- Their total profit = 2,000, and P gets 400 more than Q.
- Let Q's share = y. Then, P's share = y + 400, and y + y + 400 = 2,000 ? 2y = 1,600 ? y = 800. So P's share = 1,200.
- Thus, P:Q = 1,200:800 = 3:2.
Set up the ratio:
- (x+14,000)×8 / (x×10) = 3/2
- Cross multiply: 2(x+14,000)×8 = 3x×10
- 16x + 224,000 = 30x
- 224,000 = 14x ? x = 16,000
So, P's capital = x + 14,000 = 16,000 + 14,000 = 30,000.
Option 1: 30,000
Option 2: 6,000
Option 3: 24,000
Option 4: 20,000
- Option 1 is the correct answer.
![]()
By: Parvesh Mehta