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P started a business and invested an amount of Rs. 40,000. After 3 months, N joined her with a capital of Rs. 55,000 and after another 6 months, O joined them with a capital of Rs. 80,000. The profits at the end of the year are Rs. 16,200. Find the share of profits earned by P. 


1. Rs. 6,400
2. Rs. 5,000
3. Rs. 7,800
4. Rs. 5,200

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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.

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