Question

A, B, and C start a business, each investing ₹20{,}000. After 5 months, A withdraws ₹5{,}000, B withdraws ₹4{,}000, and C invests ₹6{,}000 more. At the end of the year, the total profit is ₹69{,}900. What is B's share of the profit?

• A. ₹20{,}500
• B. ₹21{,}200
• C. ₹28{,}200
• D. ₹27{,}300

Hint:

In partnership problems with changes during the year, use capital-months: multiply each partner’s capital by the number of months it stayed invested; profit splits in that ratio.

Answer 1

The Correct Option is B

Step 1: Time-weighted capitals (Capital $\times$ Months).
First $5$ months: all three have ₹20{,}000.
Next $7$ months (after the change):
A has ₹15{,}000; B has ₹16{,}000; C has ₹26{,}000.
Step 2: Compute each partner’s capital-months.
A: $20{,}000 \times 5 + 15{,}000 \times 7 = 100{,}000 + 105{,}000 = 205{,}000$.
B: $20{,}000 \times 5 + 16{,}000 \times 7 = 100{,}000 + 112{,}000 = 212{,}000$.
C: $20{,}000 \times 5 + 26{,}000 \times 7 = 100{,}000 + 182{,}000 = 282{,}000$.
Step 3: Ratio of profit shares and B’s amount.
Total $= 205{,}000 + 212{,}000 + 282{,}000 = 699{,}000$.
Share of B $= \dfrac{212{,}000}{699{,}000} \times ₹69{,}900 = ₹21{,}200$. \[ \boxed{₹21{,}200} \]