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 $:\text{A}$