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P invested certain money in start up for 6 months. Q invested Rs. 1,000 more than that of P for 6 months. After 6 months, P withdrew Rs. 1,000 from his capital and also Q withdrew Rs. 1,000. Ratio of profits earned at the end of one year was 37 ∶ 39. Find the amount of money invested by Q initially.


1. Rs. 19000
2. Rs. 10050
3. Rs. 20000
4. Rs. 38000

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Correct Answer - Option 3 : Rs. 20000

Given:

P invested certain money in the start-up for 6 months. Q invested Rs. 1,000 more than that of P for 6 months.

After 6 months, P withdrew Rs. 1,000 from his capital and also Q withdrew Rs. 1,000.

The ratio of profits earned at the end of one year was 37 ∶ 39.

Concepts used:

Net capital invested = Time for which capital is invested × capital invested

Calculation:

Let capital invested by P be Rs. x.

⇒ Capital invested by Q = (x + 1,000)

After 6 months, P withdrew Rs. 1,000 from his capital.

⇒ Net capital invested by P = (6 × x) + {6 × (x – 1,000)} = 12x – 6,000

⇒ Net capital invested by Q = {6 × (x + 1,000)} + {6 × (x + 1,000 - 1,000)} = 12x + 6,000

⇒ Ratio of profits of P and Q = 12x – 6,000 ∶ 12x + 6,000 = x – 500 ∶ x + 500

⇒ 37/39 = (x – 500)/(x + 500)

⇒ 37 × (x + 500) = 39 × (x – 500)

⇒ 37x + 18500 = 39x – 19500

⇒ 2x = 38000

⇒ x = Rs. 19000

⇒ Capital invested by Q = x + 1000 = 19000 + 1,000 = Rs. 20000

Q invested Rs. 20000 in the business initially.

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