Question

Rahul, Anurag and Vivek started a business together. In what proportion would the annual profit be distributed among them?
I. Rahul got one-fourth of the profit.
II. Rahul and Vivek contributed $75$% of the total investment.

• A. I alone sufficient while II alone not sufficient to answer
• B. II alone sufficient while I alone not sufficient to answer
• C. Either I or II alone sufficient to answer
• D. Both I and II are not sufficient to answer
• E. Both I and II are necessary to answer

Answer 1

The correct option is E Both I and II are necessary to answer

Let the total investment be Rs. $x$.
Then, $R=\left(\frac{x}{4}\right)$
$R+V=(\frac{75}{100}\times x)=\frac{3x}{4}$
$V=(\frac{3x}{4}-\frac{x}{4})=\frac{x}{2}$.
$\therefore A=x-(\frac{x}{4}+\frac{x}{2})=\frac{x}{4}$
$R:A:V=\frac{x}{4}:\frac{x}{4}:\frac{x}{2}=1:1:2$.
Thus, both I and II are needed to get the answer.
$\therefore$ Correct answer is (E).