Question:
A and B started a business with their initial investments of Rs.180 and X respectively. After 2 years from the start of the business, another person C joins them with investment Rs.300 and A and B invested additional amounts in the ratio of 1:5 respectively. If at the end of 5 years C receives (\(\frac{10}{33}\)) of total profit and the ratio of total profit of B to total profit of C is 7:6, what was the additional amount invested by B?
A and B started a business with their initial investments of Rs.180 and X respectively. After 2 years from the start of the business, another person C joins them with investment Rs.300 and A and B invested additional amounts in the ratio of 1:5 respectively. If at the end of 5 years C receives (\(\frac{10}{33}\)) of total profit and the ratio of total profit of B to total profit of C is 7:6, what was the additional amount invested by B?
Updated On: Aug 31, 2024
- Rs 80
- Rs 90
- Rs 200
- Rs 120
- None of these
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The Correct Option is C
Solution and Explanation
Let additional amount invested by A and B is 'a' and '5a' respectively.
Ratio of their profit = [180 * 2 + (180 + a) * 3]: [X * 2 + (X + 5a) * 3]:
[300 * 3]
Total profit = [180 * 2 + (180 + a) * 3] + [X * 2 + (X + 5a) * 3] + [300* 3] = (1800 + 18a + 5X)
Part of profit received by C = \(\frac{900}{(1800 + 18a + 5X) }\)= \(\frac{10}{33}\)
90 * 33 = 1800 + 18a + 5X
18a + 5X = 1170........ (1)
Total profit of B = [X * 2 + (X + 5a) * 3] = (15a + 5X)
Ratio = (15a + 5X): 900 =7: 6
15a + 5X = 1050......... (2)
From (1) and (2) –
3a = 120
a = 40
Additional amount invested by B = 5a = Rs.200
So, the correct option is (C): Rs 200.
Ratio of their profit = [180 * 2 + (180 + a) * 3]: [X * 2 + (X + 5a) * 3]:
[300 * 3]
Total profit = [180 * 2 + (180 + a) * 3] + [X * 2 + (X + 5a) * 3] + [300* 3] = (1800 + 18a + 5X)
Part of profit received by C = \(\frac{900}{(1800 + 18a + 5X) }\)= \(\frac{10}{33}\)
90 * 33 = 1800 + 18a + 5X
18a + 5X = 1170........ (1)
Total profit of B = [X * 2 + (X + 5a) * 3] = (15a + 5X)
Ratio = (15a + 5X): 900 =7: 6
15a + 5X = 1050......... (2)
From (1) and (2) –
3a = 120
a = 40
Additional amount invested by B = 5a = Rs.200
So, the correct option is (C): Rs 200.
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