werA and B started a business with initial investments in the ratio 5: 7. If after one year their profit were in the ratio 1: 2 and the period for A’s investment was 7 months B invested the money forOptions6 months10 months2 ½ months3 months4 months
Question
werA and B started a business with initial investments in the ratio 5: 7. If after one year their profit were in the ratio 1: 2 and the period for A’s investment was 7 months B invested the money forOptions6 months10 months2 ½ months3 months4 months
Solution
The problem is about the relationship between the amount of money invested, the time of investment, and the profit earned in a business partnership.
Let's denote:
- the initial investments of A and B as 5x and 7x, respectively,
- the time of investment of A as 7 months,
- the time of investment of B as y months,
- the profits of A and B as p1 and p2, respectively.
According to the problem, the ratio of the profits is 1:2, so we can write p1/p2 = 1/2.
The profit earned by each person is directly proportional to the product of the money invested and the time of investment. Therefore, we can write the equation:
(5x * 7) / (7x * y) = 1/2.
Solving this equation for y gives:
y = (5 * 7 * 2) / 7 = 10.
Therefore, B invested the money for 10 months.
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