A and B invest in the ratio 3 : 5. After 6months, C joins the business investing an amount equal to B’s. At the end of the year what will be the ratio of their profits?
Question
A and B invest in the ratio 3 : 5. After 6months, C joins the business investing an amount equal to B’s. At the end of the year what will be the ratio of their profits?
Solution
To solve this problem, we need to understand that the profit share in a business is directly proportional to the amount of money invested and the time for which it is invested.
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A and B invest in the ratio 3:5. This means if A invests 3 units, B invests 5 units.
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They both invest for a full year, which is 12 months.
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After 6 months, C joins the business investing an amount equal to B’s. This means C invests 5 units, but only for the remaining 6 months of the year.
Now, we calculate the investment multiplied by time for each person:
- A's share = 3 (investment) * 12 (months) = 36
- B's share = 5 (investment) * 12 (months) = 60
- C's share = 5 (investment) * 6 (months) = 30
So, the ratio of their profits at the end of the year will be 36:60:30.
We can simplify this ratio by dividing each part by the greatest common divisor, which is 6.
So the final ratio of their profits is 6:10:5.
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