# Q. 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 Q’s share out of the total profit of ₹2,000, what is the capital contributed by P?

a) ₹30,000

b) ₹26,000

c) ₹24,000

d) ₹20,000

Correct answer: a) ₹30,000

#### Question from UPSC Prelims 2024 CSAT

**Explanation : **

## Two persons P and Q

Let’s approach this problem step by step:

1) Let’s say Q’s investment is x.

Then, P’s investment is x + 14,000.

2) We know that profit is proportional to both the amount invested and the time of investment.

So, we can set up an equation:

P’s share : Q’s share = (x + 14,000) * 8 : x * 10

3) We’re told that P’s share is ₹400 more than Q’s share out of a total profit of ₹2,000.

So, P’s share = 1200 and Q’s share = 800.

4) Now we can set up the proportion:

1200 : 800 = (x + 14,000) * 8 : x * 10

5) Cross multiply:

1200 * 10x = 800 * (8x + 112,000)

12000x = 6400x + 89,600,000

6) Solve for x:

5600x = 89,600,000

x = 16,000

7) Remember, x is Q’s investment. We need to find P’s investment:

P’s investment = x + 14,000 = 16,000 + 14,000 = 30,000

Therefore, the capital contributed by P is ₹30,000.

The correct answer is a) ₹30,000.