A 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 months2 ½ months3 months10 months4 months
Question
A 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 months2 ½ months3 months10 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.
Step 1: Understand the given information A and B started a business with initial investments in the ratio 5:7. This means that if A invested 5x amount, B invested 7x amount. Their profits after one year were in the ratio 1:2. This means that if A's profit was y, B's profit was 2y. A's investment period was 7 months.
Step 2: Formulate the equation In a business, the profit earned is directly proportional to the money invested and the time period of investment. So, we can write the equation as:
(A's investment * A's time) / (B's investment * B's time) = A's profit / B's profit
Substituting the given values, we get:
(5x * 7) / (7x * B's time) = 1/2
Step 3: Solve the equation Solving the above equation for B's time, we get:
B's time = (5 * 7 * 2) / (7 * 1) = 10 months
So, B invested the money for 10 months.
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