Correct Answer - Option 1 : Rs. 6,400
Given:
P started a business and invested an amount of Rs. 40,000.
After 6 months, N joined her with the capital of Rs. 55,000 and after another 3 months, O joined them with a capital of Rs. 80,000.
The profits at the end of the year are Rs. 16,200.
Concepts used:
Net capital invested = Time for which capital is invested × capital invested
Calculation:
Net capital invested by P = 12 × Rs. 40,000 = Rs. 4,80,000
After 3 months, N joined her with capital of Rs. 55,000.
⇒ Net capital invested by N = 9 × Rs. 55,000 = 4,95,000
After another 6 months, O joined them with capital of Rs. 80,000.
⇒ Net capital invested by O = 3 × Rs. 80,000 = 2,40,000
Ratio of profits of P, N and O = Rs. 4,80,000 ∶ Rs. 4,95,000 ∶ Rs. 2,40,000
⇒ 96 ∶ 99 ∶ 48
⇒ 32 ∶ 33 ∶ 16
The profits at the end of the year are Rs. 16,200.
⇒ Profits earned by P = (32/(32 + 33 + 16)) × Rs. 16,200 = Rs. 6,400
∴ P earned Rs. 6,400 as profits.