The ratio of investments of two partners A and B is 7 : 9 and the ratio of their profits is 7 : 8.. If A invested the money for 9 months, for how much time did B invested his money? 

Correct option is A

Given:

Ratio of investments (A : B) = 7 : 9

Ratio of profits (A : B) = 7 : 8

A’s time = 9 months

We need B’s time.

Formula Used:

Profit $$\propto (\text{Investment} \times \text{Time})$$​

Solution:

​$$\frac{P_A}{P_B} = \frac{I_A \times T_A}{I_B \times T_B} \\ \ \\\frac{7}{8} = \frac{7 \times 9}{9 \times T_B} \\ \ \\\frac{7}{8} = \frac{7}{T_B} \\ \ \\T_B = 8 \, \text{months}$$​​

B invested his money for 8 months.