Question

Rahul starts a business with ₹ 8000. After $6$ months, Sanjay joins with some capital. If their profits after one year are equal, find Sanjay's investment.

• A. $₹ 17{,}500$
• B. $₹ 18{,}000$
• C. $₹ 16{,}000$
• D. $₹ 16{,}500$

Hint:

For partnership problems, profits divide in the ratio of (capital $\times$ time). Set these products equal when profits are equal.

Answer 1

The Correct Option is C

Step 1: Use capital--time (money $\times$ months).
Rahul: $8000\times 12=96000$ money-months.
Sanjay: Let capital $=S$, time $=6$ months $\Rightarrow$ $S\times 6$ money-months. 

Step 2: Equal profits $\Rightarrow$ equal capital--time.
$S\times 6=96000 \Rightarrow S=\dfrac{96000}{6}=16000$.
$\Rightarrow\ \boxed{₹ 16{,}000}.$