Question

# The ratio in which Aman and Bimal have contributed to the capital of a company is 3:4. Bimal has invested his capital for only 3 months and has received half as much profit as Aman, at the end of the year. Find out for how much time has Aman invested his capital in the company.A) 8 monthsB) 14 monthsC) 15 monthsD) 1 year

Hint- In order to solve this question first we will find out their effective investment ratio by assuming that Aman invested his money for t months and according to the given statement we will equate this ratio to an integer. Use these concepts to reach the answer.

Given that Aman and Bimal invested in a ratio $3:4$ and Bimal has invested his capital for only 3 months and has received half as much profit as Aman, at the end of the year.
Let us assume Aman has invested his capital for t months
Effective investment ratio $= 3 \times$ Aman’s investment time : $4 \times$ Bimal’s investment time
By substituting the values, we get
Effective investment ratio $= 3t:4 \times 3$
$= 3t:12 \\ = t:4 \\$
Now according to the given statement that Bimal has received half as much profit as Aman.
So profit is also divided into the same effective investment ratio. So we can write-
$\therefore \dfrac{t}{4} = \dfrac{2}{1} \\ \Rightarrow t = 8{\text{months}} \\$
Hence, Aman has invested his capital for 8 months
So, the correct answer is option A.

Note- A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.