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.