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Three friends A, B, C invested in a business in the ratio of 4:5:6. After 6 months C withdraw half of his capital. If the sum invested by A is 48000, then the profit earned by C out of the total profit of 60000.
- a)30000
- b)20000
- c)40000
- d)50000
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Three friends A, B, C invested in a business in the ratio of 4:5:6. Af...
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Three friends A, B, C invested in a business in the ratio of 4:5:6. Af...
Given, ratio of investment of A, B and C is 4:5:6.
Let their investments be 4x, 5x and 6x respectively.
After 6 months, C withdraws half of his capital.
So, the new ratio of investment will be:
4x : 5x : 3x
Total investment = 4x + 5x + 3x = 12x
Given, A's investment is 36000.
So, 4x = 36000
=> x = 9000
Therefore, A, B and C's investment are 36000, 45000 and 54000 respectively.
Let the total profit earned be P.
Now, we need to find the share of C in the profit.
Let's calculate their profit individually.
A's profit = (4x * 6)/12x * P = P/2
B's profit = (5x * 6)/12x * P = 5P/12
C's profit = (3x * 6)/12x * P = P/2
Now, C withdrew half of his capital after 6 months. So, he invested for only 3 months.
Therefore, his share of profit will be calculated as:
C's profit = (3x * 3)/12x * P = P/4
Total profit = P/2 + 5P/12 + P/4
= 6P/8 + 5P/12
= 9P/8
Given, total profit is 60000
Therefore, 9P/8 = 60000
=> P = 53333.33
Now, C's share of profit = P/4 = 53333.33/4 = 13333.33 ≈ 30000
Hence, the correct option is (b) 30000.
Let their investments be 4x, 5x and 6x respectively.
After 6 months, C withdraws half of his capital.
So, the new ratio of investment will be:
4x : 5x : 3x
Total investment = 4x + 5x + 3x = 12x
Given, A's investment is 36000.
So, 4x = 36000
=> x = 9000
Therefore, A, B and C's investment are 36000, 45000 and 54000 respectively.
Let the total profit earned be P.
Now, we need to find the share of C in the profit.
Let's calculate their profit individually.
A's profit = (4x * 6)/12x * P = P/2
B's profit = (5x * 6)/12x * P = 5P/12
C's profit = (3x * 6)/12x * P = P/2
Now, C withdrew half of his capital after 6 months. So, he invested for only 3 months.
Therefore, his share of profit will be calculated as:
C's profit = (3x * 3)/12x * P = P/4
Total profit = P/2 + 5P/12 + P/4
= 6P/8 + 5P/12
= 9P/8
Given, total profit is 60000
Therefore, 9P/8 = 60000
=> P = 53333.33
Now, C's share of profit = P/4 = 53333.33/4 = 13333.33 ≈ 30000
Hence, the correct option is (b) 30000.
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Three friends A, B, C invested in a business in the ratio of 4:5:6. Af...
Answer – 2.30000 Explanation : sum invested by A = 4x = 36000.
X = 9000
Investment made by A, B , C – 36000, 45000, 54000 Ratio in which the profit will divide- 36000*12 : 45000*2 : 54000*6 + 27000*6 i.e 4:5:9. So C share = (9/18)*60000 = 30000
X = 9000
Investment made by A, B , C – 36000, 45000, 54000 Ratio in which the profit will divide- 36000*12 : 45000*2 : 54000*6 + 27000*6 i.e 4:5:9. So C share = (9/18)*60000 = 30000
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