Arithmetic

Ratio, Proportion & Variation

Medium

A, B and C started a business by investing in the ratio 4:3:2. At the end of the year the profit earned was distributed among them in the ratio 8:9:10. Find the ratio of the durations of their investment.

5 : 6 : 8

2 : 3 : 5

2 : 3 : 4

3 : 4 : 6

✅ Correct Option: 2

Profit ratio = Investment $\times$ Time ratio. So time ratio $=\frac{\text{profit}}{\text{investment}}=\frac{8}{4}:\frac{9}{3}:\frac{10}{2}=2:3:5$ .

Note: The chosen option 1 (5:6:8) is incorrect; the correct answer is option 2 (2:3:5).

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