Discussion
Bharati started a business with ₹ 18,000 and Manju joined it afterwards with ₹ 36,000. Find out after how many months did Manju joined the business, if profit were distributed equally after the end of a year.
Answer: D
Manju joined after 6 months.
Profits are shared in the ratio of capital multiplied by time. Equal shares mean equal products. Bharati invested for 12 months; let Manju invest for \(m\) months:
\[ \begin{aligned} 18000 \times 12 &= 36000 \times m \\ m &= 6 \end{aligned} \]
Manju's money was at work for 6 months, so she joined 12 - 6 = 6 months after the start. Joining after 10, 5 or 8 months would leave her capital working for 2, 7 or 4 months, giving products of 72,000, 252,000 or 144,000 against Bharati's 216,000.
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