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

Step 1: Capital-month products: \( A=16000\times3+11000\times9=147000 \), \( B=12000\times3+17000\times9=189000 \), \( C=21000\times6=126000 \), giving ratio \( 147000:189000:126000=7:9:6 \).

Step 2: Total profit \( ₹26{,}400 \) split in \( 22 \) parts gives one part \( =\dfrac{26400}{22}=₹1200 \).

Step 3: So \( B=9\times1200=₹10{,}800 \) and \( C=6\times1200=₹7{,}200 \), and their difference is \[ 10800-7200=₹3600. \]
\[ \boxed{₹3600} \]