Question

P and Q invested in a venture in the ratio 4:7. The profit was shared in the ratio 8:7. If P invested for 14 months, for how long did Q invest?

• A. 6 months
• B. 7 months
• C. 8 months
• D. 9 months

Answer 1

Answer:

B. 7 months

To find out how long Q invested, we can use the fundamental rule of partnerships: Profit is shared in the ratio of the product of capital (investment) and time.

Let:

• Capital of P ($C_1$) = $4x$

• Capital of Q ($C_2$) = $7x$

• Time of P ($T_1$) = $14$ months

• Time of Q ($T_2$) = $t$ months

• Ratio of profits = $\frac{8}{7}$

Step-by-Step Calculation:

1. Set up the profit ratio formula:

   $\frac{\text{Profit of P}}{\text{Profit of Q}} = \frac{C_1 \times T_1}{C_2 \times T_2}$

2. Substitute the given values into the formula:

   
   $\frac{8}{7} = \frac{4 \times 14}{7 \times t}$

3. Simplify and solve for $t$:

   
   $\frac{8}{7} = \frac{56}{7t}$

   Cross-multiply to solve for $t$:

   $8 \times (7t) = 7 \times 56$

   $56t = 392$

   $t = \frac{392}{56}$

   $t = 7$

Answer: Q invested for 7 months.