Question:
Two persons A and B started a business with B's investment exceeding that of A by ₹6000. At the end of 8 months from the start of the business B left it and another person C joined the business with investment exceeding that of A by ₹8000. If the ratio between the total annual profit and B's share in the profit was 2:1, then A's investment in ₹ is
Two persons A and B started a business with B's investment exceeding that of A by ₹6000. At the end of 8 months from the start of the business B left it and another person C joined the business with investment exceeding that of A by ₹8000. If the ratio between the total annual profit and B's share in the profit was 2:1, then A's investment in ₹ is
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For partnership questions, first calculate Investment × Time for each partner. Profit sharing is always proportional to these products.
Updated On: Jun 15, 2026
- 3000
- 2600
- 2400
- 2000
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The Correct Option is D
Solution and Explanation
Concept:
In partnership problems, profit is distributed in the ratio of
\[
\text{Investment} \times \text{Time}
\]
for each partner.
Step 1: Assume A's investment.
Let A's investment be \[ ₹x \] Then \[ \text{B's investment}=x+6000 \] and \[ \text{C's investment}=x+8000 \]
Step 2: Compute investment-time products.
A remains throughout the year. \[ A=12x \] B remains for 8 months. \[ B=8(x+6000) \] \[ =8x+48000 \] C joins after 8 months and remains for 4 months. \[ C=4(x+8000) \] \[ =4x+32000 \]
Step 3: Form the profit ratio.
Total profit ratio \[ =12x+(8x+48000)+(4x+32000) \] \[ =24x+80000 \] Given \[ \frac{\text{Total Profit}}{\text{B's Share}} = \frac{2}{1} \] Hence \[ \frac{24x+80000}{8x+48000}=2 \]
Step 4: Solve for \(x\).
\[ 24x+80000=16x+96000 \] \[ 8x=16000 \] \[ x=2000 \] Therefore A's investment is \[ \boxed{₹2000} \]
Step 1: Assume A's investment.
Let A's investment be \[ ₹x \] Then \[ \text{B's investment}=x+6000 \] and \[ \text{C's investment}=x+8000 \]
Step 2: Compute investment-time products.
A remains throughout the year. \[ A=12x \] B remains for 8 months. \[ B=8(x+6000) \] \[ =8x+48000 \] C joins after 8 months and remains for 4 months. \[ C=4(x+8000) \] \[ =4x+32000 \]
Step 3: Form the profit ratio.
Total profit ratio \[ =12x+(8x+48000)+(4x+32000) \] \[ =24x+80000 \] Given \[ \frac{\text{Total Profit}}{\text{B's Share}} = \frac{2}{1} \] Hence \[ \frac{24x+80000}{8x+48000}=2 \]
Step 4: Solve for \(x\).
\[ 24x+80000=16x+96000 \] \[ 8x=16000 \] \[ x=2000 \] Therefore A's investment is \[ \boxed{₹2000} \]
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