Question

P and Q started a business in partnership by investing in the ratio of 7 : 9. After 4 months P withdraw 1/3 of its money and after 6 months from starting, Q withdraws 33 1/3 % of its money. If a total earned profit is Rs. 18,500 at the end of 9 months, find the share of P in profit.

1. Rs. 7,700 
2. Rs. 8,000
3. Rs. 9,000
4. Rs. 9,500
5. None of these 

Answer 1

Correct Answer - Option 1 : Rs. 7,700 

Given that: 

Ratio of Money invested by P and Q = 7 : 9

Total profit at the end of 9 months = Rs. 18,500

Formula Used:

Profit = time × money

Investment ratio is equal to profit ratio

Calculation:

Let the money of P and Q = 7 × 3z = 21z,   9 × 3z = 27z

Total capital invested by P in 9 months

⇒ (21z × 4) +(2/3 of 21z) × 5 = 154z

Total capital invested by Q in 9 months

⇒ (27z × 6) + ( 2/3 of 27z ) × 3 = 216z

So, the profit ratio of P and Q = 154z : 216z = 77z : 108z

According to question,

(77z + 108z) = Rs. 18500

⇒ 185z = Rs. 18500

⇒ z = Rs. 100

So, the share of P in profit = 77 × 100 = Rs. 7700 

The share of Q = 108 × 100 = Rs. 10,800 

∴ The share of P is Rs. 7700