Pablo and Quezon each invested some money in a business in the ratio of 4:7 respectively. After six months, Pablo

[Mikrislac]

Pablo and Quezon each invested some money in a business in the ratio of 4:7 respectively. After six months, Pablo withdrew his invested capital. If Pablo and Quezon each received profits in the ratio of 4:21, then for how many months did Quezon invest in the business?

A. 5
B. 7
C. 12
D. 18
E. 21

[Mikrislac]

Profit (P) earned by an investor is equal to their amount of investment (I) multiplied by the amount of time they invested (T).

P = I*T

This means that that for two investors, the profits earned will be in the following ratio:

P1/P2 = I1*T1/(I2*T2)

Here P1 = 4 units * 6 months = 4 (given) and P2 = 7 units * x months = 21 (given).

P1/P2 = 4/21 = 4*6/(7*x). Solve for x: x = 18 months.

Answer: D