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A started business with investment ₹5000...

A started business with investment `₹5000` after 2 months B,C joined with `₹2500` and `₹3,500` resp, if total profit was `₹4,800` what was B's share in annual profit ?

A

`₹1150`

B

`₹1000`

C

`₹1050`

D

`₹1820`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will calculate the share of B in the total profit based on their investments and the time they invested in the business. ### Step 1: Calculate the effective investment of A, B, and C. - A's investment: ₹5000 for 12 months - B's investment: ₹2500 for 10 months (joined after 2 months) - C's investment: ₹3500 for 10 months (joined after 2 months) ### Step 2: Calculate the total investment in terms of "investment-months". - A's contribution: \[ 5000 \times 12 = 60000 \text{ investment-months} \] - B's contribution: \[ 2500 \times 10 = 25000 \text{ investment-months} \] - C's contribution: \[ 3500 \times 10 = 35000 \text{ investment-months} \] ### Step 3: Calculate the total investment-months. \[ \text{Total investment-months} = 60000 + 25000 + 35000 = 120000 \] ### Step 4: Determine the ratio of their investments. The ratio of A, B, and C's contributions in investment-months is: \[ A : B : C = 60000 : 25000 : 35000 \] To simplify this ratio, we can divide each term by 5000: \[ = 12 : 5 : 7 \] ### Step 5: Calculate the total parts in the ratio. \[ \text{Total parts} = 12 + 5 + 7 = 24 \] ### Step 6: Calculate B's share of the profit. Given that the total profit is ₹4800, we can find B's share using the ratio: \[ \text{B's share} = \left(\frac{5}{24}\right) \times 4800 \] Calculating B's share: \[ = \frac{5 \times 4800}{24} = \frac{24000}{24} = 1000 \] ### Final Answer: B's share in the annual profit is ₹1000. ---
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