Question:
A person A started a business by investing ₹40000. After 3 months another person B joined him by investing ₹50000. After a few months another person C joined them by investing ₹60000. At the end of the year they shared their profits in the ratio \(16:15:14\). When did C join the business?
A person A started a business by investing ₹40000. After 3 months another person B joined him by investing ₹50000. After a few months another person C joined them by investing ₹60000. At the end of the year they shared their profits in the ratio \(16:15:14\). When did C join the business?
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In partnership questions always use:
\[
\text{Profit Share} \propto \text{Capital} \times \text{Time}.
\]
Never compare capitals alone.
Updated On: Jun 12, 2026
- After 3 months
- After 4 months
- After 5 months
- After 7 months
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The Correct Option is C
Solution and Explanation
Concept:
In partnership problems, profit sharing ratio is proportional to:
\[
\text{Capital} \times \text{Time}
\]
Step 1: Calculate capital-time products for A and B. A invested ₹40000 for entire 12 months. \[ 40000 \times 12 = 480000 \] B joined after 3 months. Hence B invested for \[ 12-3=9 \text{ months} \] \[ 50000 \times 9 = 450000 \] These are proportional to \[ 16:15 \] which agrees with the given ratio.
Step 2: Determine the investment period of C. Let C invest for \(t\) months. \[ 60000t \] According to the profit ratio, \[ 480000:450000:60000t = 16:15:14 \] Using A and C: \[ 480000:60000t = 16:14 \] \[ \frac{8}{t} = \frac{16}{14} \] \[ 112=16t \] \[ t=7 \] Thus C invested for 7 months. Therefore C joined after \[ 12-7=5 \] months. \[ \boxed{\text{After 5 months}} \]
Step 1: Calculate capital-time products for A and B. A invested ₹40000 for entire 12 months. \[ 40000 \times 12 = 480000 \] B joined after 3 months. Hence B invested for \[ 12-3=9 \text{ months} \] \[ 50000 \times 9 = 450000 \] These are proportional to \[ 16:15 \] which agrees with the given ratio.
Step 2: Determine the investment period of C. Let C invest for \(t\) months. \[ 60000t \] According to the profit ratio, \[ 480000:450000:60000t = 16:15:14 \] Using A and C: \[ 480000:60000t = 16:14 \] \[ \frac{8}{t} = \frac{16}{14} \] \[ 112=16t \] \[ t=7 \] Thus C invested for 7 months. Therefore C joined after \[ 12-7=5 \] months. \[ \boxed{\text{After 5 months}} \]
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