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A, B and C entered into a partnership. A invested Rs. 2560 and B invested Rs. 2000. At the end of the year, they gained Rs. 1105, out of which A got Rs. 320. C's capital was ?
  • a)
    Rs. 2840
  • b)
    Rs. 4028
  • c)
    Rs. 4280
  • d)
    Rs. 4820
Correct answer is option 'C'. Can you explain this answer?
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A, B and C entered into a partnership. A invested Rs. 2560 and B inves...
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A, B and C entered into a partnership. A invested Rs. 2560 and B inves...
Given:
A's investment = Rs. 2560
B's investment = Rs. 2000
Total profit = Rs. 1105
A's share of profit = Rs. 320

Let's assume C's capital as 'x'.

To find C's capital, we can use the concept of ratio and proportion.

Step 1: Calculate the total investment
Total investment = A's investment + B's investment + C's investment
Total investment = Rs. 2560 + Rs. 2000 + Rs. x
Total investment = Rs. 4560 + x

Step 2: Calculate the ratio of each partner's investment
Ratio of A's investment : B's investment : C's investment
= Rs. 2560 : Rs. 2000 : Rs. x
= 2560/2000 : 2000/2000 : x/2000
= 32/25 : 1 : x/2000

Step 3: Calculate the ratio of each partner's profit
Ratio of A's profit : B's profit : C's profit
= Rs. 320 : (Total profit - A's profit) : (Total profit - A's profit)
= 320 : (1105 - 320) : (1105 - 320)
= 320 : 785 : 785
= 320/785 : 785/785 : 785/785
= 64/157 : 1 : 1

Step 4: Equate the ratio of investments to the ratio of profits
32/25 : 1 : x/2000 = 64/157 : 1 : 1

Cross-multiplying,
(32/25) * (1) * (2000) = (64/157) * (1) * (x)
2560/25 = 64/157 * x
102.4 = 0.408 * x
x = 102.4 / 0.408
x = 2512

Therefore, C's capital is Rs. 2512.
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Question Description
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