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Partnership

A and B start a business with capital of Rs. 25,000 and Rs. 35,000. After 5 months, C joins with Rs. 40,000. After another 3 months, A withdraws Rs. 5

Question

A and B start a business with capital of Rs. 25,000 and Rs. 35,000. After 5 months, C joins with Rs. 40,000. After another 3 months, A withdraws Rs. 5,000, and B adds Rs. 10,000, while C continues with the same. At the end of a year, the profit is Rs. 60,000. Find the exact share of profit of C. (within 2 decimal)

Rs. 16,470.59

Rs. 19,550.24

Rs. 22,780.24

Rs. 31,670.24

Solution

Correct option is A

Given:
A's initial capital = Rs. 25,000
B's initial capital = Rs. 35,000
C's capital = Rs. 40,000 (after 5 months)
Total profit at the end of the year = Rs. 60,000
Formula Used:
Profit Ratio = Ratio of the product of Investment and Time
Solution:
A's investment is Rs. 25,000 for the first 8 months. After withdrawing Rs. 5,000, his investment is Rs. 20,000 for the remaining 4 months.
A's equivalent capital = 25000 × 8 + 20000 × 4
200000 + 80000 = 280000
B's investment is Rs. 35,000 for the first 8 months. After adding Rs. 10,000, his investment is Rs. 45,000 for the remaining 4 months.
B's equivalent capital = 35000 × 8 + 45000 × 4
280000 + 180000 = 460000
C joins after 5 months, so his investment is Rs. 40,000 for the remaining 7 months of the year.
C's equivalent capital = 40000 × 7 = 280000
Ratio of profit shares of A, B, and C:
280000 : 460000 : 280000
= 14 : 23 : 14
Total ratio units = 14 + 23 + 14 = 51
Share of C = $\frac{14}{51}$ × 60000
Share of C = 16470.588...
Rounding to two decimal places, C's share is Rs. 16470.59
Final Answer
So the correct answer is (a)