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}.