Question

A and B entered into a partnership, investing ₹$16000$ and ₹$12000$ respectively. After $3$ months, A withdrew ₹$5000$ while B invested ₹$5000$ more. After $3$ more months, C joined with ₹$21000$. At the end of a year, the profit was ₹26,400. By how much does B's share exceed C's share?
 

• A. 3600
• B. 2100
• C. 3000
• D. 2300

Hint:

For partnerships with changing capitals, always use capital × time to form the profit ratio.
 

Answer 1

The Correct Option is A

Use time–capital products (in ₹–months).
A: \(16000\) for \(3\) months, then \(11000\) for \(9\) months \(\Rightarrow 16000\cdot 3+11000\cdot 9=147000.\) 
B: \(12000\) for \(3\) months, then \(17000\) for \(9\) months \(\Rightarrow 12000\cdot 3+17000\cdot 9=189000.\) 
C: joins at month \(6\) with \(21000\) for \(6\) months \(\Rightarrow 21000\cdot 6=126000.\) 
So the ratio \(A:B:C=147000:189000:126000=7:9:6.\) One share \(=\dfrac{26400}{7+9+6}=\dfrac{26400}{22}=1200.\) 
Thus \(B=9\times1200=10800,\ C=6\times1200=7200.\) Excess \(=10800-7200=\boxed{3600}.\)