Three men entered into a business in partnership for 14 months, 8 months and 7 months. If the ratio of their profit is 5 : 7 : 8, what is the ratio of their investments?

Correct option is A

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Given:

Profit ratio of P1 : P2: P3 = 5 : 7 : 8

Time T1 =  14 months , T2 = 8 months , T3 =  7 months

Solution:

let the investment be A , B and C.

we know that the ratio of investments is proportional to the ratio = Profit/Time

$$\text{So, } \frac{A}{B} = \frac{P_1/T_1}{P_2/T_2} = \frac{5/14}{7/8} = \frac{5 \times 8}{7 \times 14} = \frac{40}{98} = \frac{20}{49}. \\\frac{B}{C} = \frac{P_2/T_2}{P_3/T_3} = \frac{7/8}{8/7} = \frac{7 \times 7}{8 \times 8} = \frac{49}{64}. \\$$​​

therefore, the ratio of investment is 20:49:64