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Three partners P,Q,R run business with i...

Three partners P,Q,R run business with investments of 30,000,40,000,and 50,000 resp P stays for entire year Q leave s the business after two months but rejoin ater 4 months but with only 3/4 of initial capital and R leaves after 3 months and rejoins after 5 months but with 4/5 of initial capital .If at the end of year,the profit is Rs27,900 then how much did R get more than Q in profit

A

`₹2000`

B

`₹1.250`

C

`₹1,500`

D

`₹1000`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, let's break down the investments and the time each partner spent in the business. ### Step 1: Calculate the effective capital contribution of each partner. 1. **Partner P**: - Investment = Rs 30,000 - Time = 12 months (entire year) - Effective capital contribution = 30,000 * 12 = Rs 360,000 2. **Partner Q**: - Investment = Rs 40,000 - Time = 2 months (initially) + 6 months (after rejoining with 3/4 capital) - Effective capital contribution for the first 2 months = 40,000 * 2 = Rs 80,000 - New investment after rejoining = 40,000 * (3/4) = Rs 30,000 - Effective capital contribution for the next 10 months = 30,000 * 10 = Rs 300,000 - Total effective capital contribution = Rs 80,000 + Rs 300,000 = Rs 380,000 3. **Partner R**: - Investment = Rs 50,000 - Time = 3 months (initially) + 4 months (after rejoining with 4/5 capital) - Effective capital contribution for the first 3 months = 50,000 * 3 = Rs 150,000 - New investment after rejoining = 50,000 * (4/5) = Rs 40,000 - Effective capital contribution for the next 9 months = 40,000 * 9 = Rs 360,000 - Total effective capital contribution = Rs 150,000 + Rs 360,000 = Rs 510,000 ### Step 2: Calculate the total effective capital contributions. - Total effective capital contributions = P + Q + R - Total = Rs 360,000 + Rs 380,000 + Rs 510,000 = Rs 1,250,000 ### Step 3: Determine the profit share of each partner. The total profit is Rs 27,900. The profit share of each partner is proportional to their effective capital contributions. 1. **Profit share of P**: - P's share = (360,000 / 1,250,000) * 27,900 = Rs 10,032 2. **Profit share of Q**: - Q's share = (380,000 / 1,250,000) * 27,900 = Rs 11,064 3. **Profit share of R**: - R's share = (510,000 / 1,250,000) * 27,900 = Rs 6,804 ### Step 4: Calculate how much more R got than Q. - Difference = R's share - Q's share = Rs 6,804 - Rs 11,064 = Rs -4,260 Since R's share is less than Q's, we need to find how much more Q got than R. ### Final Calculation: - Q got more than R = Rs 11,064 - Rs 6,804 = Rs 4,260 ### Conclusion: R did not get more than Q; instead, Q got Rs 4,260 more than R.
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