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The revenue and expenditure of four different companies $\text{P, Q, R and S}$ in $2015$ are shown in the figure. If the revenue of company $\text{Q}$ in $2015$ was $20$% more than that in $2014$, and company $\text{Q}$ had earned a profit of $10$% on expenditure in $2014$, then its expenditure (in million rupees) in $2014$ was _______.

              

  1. $32.7$
  2. $33.7$
  3. $34.1$
  4. $35.1$
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Let the revenue of company $Q$ in $2014$ be $₹ x.$

Then the revenue of company $Q$ in $2015 = x + x \times \frac{20}{100} = \frac{120x}{100} = 1.2x$

Now, $1.2x = 45$

$\implies x = \frac{45}{1.2} = 37.50$

Given that, the company $Q$ had earned a profit of $10\%$ on expenditure in $2014.$

Let the expenditure of company $Q$ in $2014$ be $₹ x.$

The company $Q$ earn $10\%$ profit on it’s expenditure and this profit adds to the revenue of company $Q.$

Now, $y+y\times \frac{10}{100} = 37.50$

$\implies \frac{110y}{100} = 37.50$

$\implies \frac{11y}{10} = 37.50$

$\implies 11y = 375 . 0$

$\implies y = \frac{375.0}{11} = 34.0909 \approx ₹ 34.1$


$\textbf{Short Method:}$ Let the revenue of company $Q$ in $2014$ be $₹ 100.$

Then the revenue of company $Q$ in $2015 = ₹ 120$

  • $120 \longrightarrow 45$
  • $100 \longrightarrow 37.50$

The company $Q$ earn $10\%$ profit on its expenditure and this profit adds to the revenue of company $Q.$

Let  the expenditure of company $Q$ in $2014$ be $₹ y.$

$\frac{110y}{100} = 37.50$

$\implies y = ₹ 34.1$

So, the correct answer is $(C).$

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Ans C.

Revenue of Company Q in 2015 = 45 (million rupees)

Let the revenue of Company Q in 2014 = $x$ (million rupees)

Then the revenue of company Q in 2015 = $1.2 x $ (million rupees)

$1.2 x  = 45, x = 37.5$  (million rupees)

Given Q has earned profit of 10% on expenditure (y) in 2014 ( which becomes its revenue)

$ 1.1 y = 37.5 , y = 34.09 \approx 34.1 $

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