Questions & Answers

Question

Answers

A) 8 months

B) 14 months

C) 15 months

D) 1 year

Answer
Verified

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.

__Complete step-by-step 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.

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.

×

Sorry!, This page is not available for now to bookmark.