Question

If the expenditures of Companies X and Y in 1996 were equal and the total income of the two Companies in 1996 was Rs. 342 crores, what was the total profit of the two Companies together in 1996? (Profit = Income - Expenditure)

• A. Rs. 240 crores
• B. Rs. 171 crores
• C. Rs. 120 crores
• D. Rs. 102 crores
• E. None of these

Answer 1

The correct option is D

Rs. 102 crores

Let the expenditures of each of the Companies X and Y in 1996 be Rs. x crores.

And let the income of Company X in 1996 be Rs. z crores so that the income of Company Y in 1996 = Rs. (342 - z) crores.

Then, for Company X we have :

$\begin{array}{cc}40=\frac{z-x}{x}\times 100\Rightarrow \frac{40}{100}=\frac{z}{x}-1\Rightarrow x=\frac{100z}{140}& ...\left(i\right)\\ Also,forCompanyYwehave;& \\ 45=\frac{\left(342-z\right)-x}{x}\times 100\Rightarrow \frac{45}{100}=\frac{\left(342-z\right)}{x}-1\Rightarrow \frac{\left(342-z\right)\times 100}{145}& ...\left(ii\right)\\ From\left(i\right)and\left(ii\right),weget:\frac{100z}{140}=\frac{\left(342-z\right)\times 100}{145}\Rightarrow z=168& \end{array}$

Substituting z = 168 in (i), we get : x = 120.

$\therefore$ Total expenditure of Companies X and Y in 1996 = 2x = Rs. 240 crores.

Total income of Companies X and Y in 1996 = Rs. 342 crores.

$\therefore$ Total profit = Rs. (342 - 240) crores = Rs. 102 crores.