elect the correct answerA 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 forOptions10 months2 ½ months3 months6 months4 months
Question
elect the correct answerA 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 forOptions10 months2 ½ months3 months6 months4 months
Solution
The problem states that A and B started a business with initial investments in the ratio 5:7. The profit after one year was in the ratio 1:2. The period for A’s investment was 7 months. We need to find out for how long B invested the money.
The formula for calculating the profit ratio is (Investment of A * Time of A) : (Investment of B * Time of B).
We know the investment ratio and the profit ratio, and we know the time A invested. We can set up the equation and solve for the time B invested.
(Investment of A * Time of A) : (Investment of B * Time of B) = Profit ratio
Substituting the given values into the equation:
(5 * 7) : (7 * Time of B) = 1 : 2
Solving the equation gives:
35 : (7 * Time of B) = 1 : 2
Cross multiplying to solve for Time of B gives:
35 * 2 = 7 * Time of B
70 = 7 * Time of B
Time of B = 70 / 7
Time of B = 10 months
So, B invested the money for 10 months.
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