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Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
- a)5 : 7 : 8
- b)20 : 49 : 64
- c)38 : 28 : 21
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Three partners shared the profit in a business in the ratio 5 : 7 : 8....
Given, ratio of profit sharing = 5 : 7 : 8
Let the investments of the partners be 5x, 7x, and 8x respectively.
Total profit = profit of A + profit of B + profit of C
Let the profit of A be P.
Then, profit of B = 7/5P and profit of C = 8/5P
Now, let us calculate the time period for which the partners invested their money.
A invested for 14 months, B invested for 8 months and C invested for 7 months.
Total time period = 14 + 8 + 7 = 29 months
Now, we know that the profit is directly proportional to the time period.
Therefore, P/14 = 7/5P/8 = 8/5P/7
Solving the above equation, we get P = 14k, where k is a constant.
Therefore, profit of A = 14k, profit of B = 98k/35 and profit of C = 112k/35
Total profit = 14k + 98k/35 + 112k/35 = 84k/5
We know that the ratio of profit sharing is equal to the ratio of their investments.
Therefore, (14k)/(5x) = (98k/35)/(7x) = (112k/35)/(8x)
Solving the above equation, we get x = 4
Therefore, the investments of the partners are 5x = 20, 7x = 28, and 8x = 32.
Hence, the ratio of their investments is 20 : 49 : 64. Thus, option (b) is the correct answer.
Let the investments of the partners be 5x, 7x, and 8x respectively.
Total profit = profit of A + profit of B + profit of C
Let the profit of A be P.
Then, profit of B = 7/5P and profit of C = 8/5P
Now, let us calculate the time period for which the partners invested their money.
A invested for 14 months, B invested for 8 months and C invested for 7 months.
Total time period = 14 + 8 + 7 = 29 months
Now, we know that the profit is directly proportional to the time period.
Therefore, P/14 = 7/5P/8 = 8/5P/7
Solving the above equation, we get P = 14k, where k is a constant.
Therefore, profit of A = 14k, profit of B = 98k/35 and profit of C = 112k/35
Total profit = 14k + 98k/35 + 112k/35 = 84k/5
We know that the ratio of profit sharing is equal to the ratio of their investments.
Therefore, (14k)/(5x) = (98k/35)/(7x) = (112k/35)/(8x)
Solving the above equation, we get x = 4
Therefore, the investments of the partners are 5x = 20, 7x = 28, and 8x = 32.
Hence, the ratio of their investments is 20 : 49 : 64. Thus, option (b) is the correct answer.
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Community Answer
Three partners shared the profit in a business in the ratio 5 : 7 : 8....
Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x : 8y : 7z = 5 : 7 : 8.
Then, 14x : 8y : 7z = 5 : 7 : 8.
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Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?a)5 : 7 : 8b)20 : 49 : 64c)38 : 28 : 21d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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