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CAT 2017 Set-1 | Question: 74

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Suppose, $\text{C1, C2, C3, C4}$, and $\text{C5}$ are five companies. The profits made by $\text{C1, C2}$, and $\text{C3}$ are in the ratio $9: 10: 8$ while the profits made by $\text{C2, C4}$, and $\text{C5}$ are in the ratio $18: 19: 20$. If $\text{C5}$ has made a profit of Rs $19$ crore more than $\text{C1}$, then the total profit (in Rs) made by all five companies is

  1. $438$ crore
  2. $435$ crore
  3. $348$ crore
  4. $345$ crore

1 Answer

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Given that,  $\text{C1, C2, C3, C4}$ and $\text{C}5$ are five companies,      

  • $ \text{C1 : C2 : C3} = 9 : 10 : 8 \quad \longrightarrow (1)$     
  • $ \text{C2 : C4 : C5} = 18  : 19 : 20 \quad \longrightarrow (2)$ 

From equation $(1),$ we can write

  • Profit of $\text{C}1 = 9x$
  • Profit of $\text{C}2 = 10x$
  • Profit of $\text{C}3 = 8x$

From equation $(1),$ we can write

  • Profit of $\text{C}2 = 18y$
  • Profit of $\text{C}4 = 19y$
  • Profit of $\text{C}5 = 20y$

According to the question, $\text{C}5$ has made a profit of Rs $19$ crore more than $\text{C}1.$

Then, $\text{C}5 = \text{C1} + 19$

$\Rightarrow \text{C5 – C1} = 19$ 

$\Rightarrow 20y – 9x = 19 \quad \longrightarrow (3)$ 

The profit of $\text{C}2$ should be equal.

$10x = 18y$

$\Rightarrow 5x = 9y$

$\Rightarrow x  = \dfrac{9y}{5}$

Put the value of $x$, in the equation $(3),$ we get.

$20y – 9x = 19$

$\Rightarrow 20y – 9\left(\frac{9y}{5}\right) = 19$

$\Rightarrow 100y – 81y = 95$

$\Rightarrow 19y = 95$

$\Rightarrow \boxed{y = 5}$

So, $x = \frac{9(5)}{5}$

$\Rightarrow \boxed{x = 9}$

Now, we can calculate the profit of all of the five companies.

  • Profit of $\text{C}1 = 9x = 81$
  • Profit of $\text{C}2 = 10x = 90$
  • Profit of $\text{C}3 = 8x = 72$
  • Profit of $\text{C}4 = 19y = 95$
  • Profit of $\text{C}5 = 20y = 100$

$\therefore$ The total profit (in Rs) made by all five companies $ = 81 + 90 + 72 + 95 + 100 = 438$ crores.

Correct Answer $:\text{A}$

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