Question

A and B invested in a business in the ratio 5:6. The profit ratio was 10:9. If B invested his money for 12 months, for how many months did A invest?

• A. 15 months
• B. 16 months
• C. 12 months
• D. 11 months

Answer 1

Answer:

B. 16 months

Profit is proportional to Investment × Time.

Given:

• Investment ratio (A:B = 5:6)

• Profit ratio (A:B = 10:9)

• B invested for 12 months

• Let A invest for (x) months.

Using:

$\frac{\text{Profit of A}}{\text{Profit of B}}$

$\frac{5 \times x}{6 \times 12}$

$\frac{10}{9}$

So,

$\frac{5x}{72}=\frac{10}{9}$

Cross-multiply:

$5x \times 9 = 72 \times 10$

45x = 720

$x = \frac{720}{45} = 16$

Answer:

$\boxed{16\text{ months}}$