A garage owner brought a certain amt of petrol for Rs450. if petrol costs Rs x per litre ,write down the expression for no. of litres of petrol obtained. When the price per litre increases by Rs 5 per litre, he found that he obtained 3 litres less for the same sum of money. find the original price of petrol per litre.

Answer :

Given  : A garage owner bought a certain amount of petrol for Rs.450 and  petrol costs Rs. x per litre .

So,

Quantity of petrol bought from Rs 450  = $\frac{450}{x}$ litres

When the price per litre increases by Rs 5 per litre, then

Quantity of petrol bought from Rs 450 = $\frac{450}{x + 5}$ litres

But he found that he obtained 3 litres less for the same sum of money. So, we get

$\frac{450}{x}$  - 3  = $\frac{450}{x + 5}$

$$\begin{gathered} \Rightarrow \frac{450}{x} - 3 = \frac{450}{x + 5} \\ \Rightarrow \frac{450 - 3x}{x} = \frac{450}{x + 5} \\ \Rightarrow \left( 450 - 3x \right)\left( x + 5 \right) = 450x \\ \Rightarrow 450x +\hspace{0.17em}2250- 3x^2 - 15x = 450x \\ \Rightarrow - 3x^2 - 15x + 2250 = 0 \\ \Rightarrow - 3\left( x^2 + 5x - 750 \right) = 0 \\ \Rightarrow x^2 + 5x - 750 = 0 \\ \Rightarrow x^2 +30x -25x - 750 = 0 \\ \Rightarrow x \left( x+30\right) -25 \left( x+30\right) = 0 \\ \Rightarrow \left( x - 25 \right) \left( x+30\right) = 0 \end{gathered}$$
So,
x  = 25 and  - 30 
And we take x as price of petrol per litre , So , x can't be negative , Then we neglect x  = - 30  and get
x  = 25
So,
Original price of petrol per litre  = Rs  25                                                        ( Ans )