A and B entered into a partnership by investing ₹16000 and ₹12000 respectively. After 3 months, A withdrew ₹5000 while B invested ₹5000 more. After 3 more months, C joined the business with a capital of ₹21000. If after one year, the profit is ₹26400, then by how much does the share of B in the profit exceed that of C?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → ₹3600
Profit is shared in the ratio of each partner’s capital multiplied by the time it was in the business. When a capital changes during the year, each part is multiplied by its own number of months.
Capital × months for each partner (12 months in all):
A: 16000 for 3 months, then \(16000-5000=11000\) for 9 months: \(48000+99000=147000\)
B: 12000 for 3 months, then \(12000+5000=17000\) for 9 months: \(36000+153000=189000\)
C: joins after \(3+3=6\) months, so 21000 for 6 months: \(126000\)
Sharing the profit of ₹26400:
Ratio \(147000:189000:126000=7:9:6\) (dividing by 21000)
One share \(\displaystyle =\frac{26400}{7+9+6}=\frac{26400}{22}=1200\)
B’s share exceeds C’s by \(9-6=3\) shares: \(3\times1200=3600\), that is, ₹3600