Question

A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for rupees 180. Find the original price of the petrol

Answer 1

Answer:

Let X be no of litres of petrol & n be the price per litre

Eqn 1 : x*n = 180

Eqn 2 : (x+5) * (0.9n) = 180

Simplifying eqn 2

0.9xn + 4.5n = 180

Substituting eqn 1 in eqn 2

0.9 ( 180) + 4.5n = 180

n = 18/4.5 = 4

Hence E

Answer 2

The original price of petrol is  Rs.4 per gallon.

Step-by-step explanation:

Given:

The price of petrol reduction by 10%.

A motorist to buy 5 gallons more for rupees 180.

To Find:

The original price of petrol.

Solution:

Let the original petrol price is p.

The initial volume of petrol    $=\frac{180}{p}$    gallons

As given - The price of petrol reduction by 10%.

Reduction of price of petrol by 10% means, new price of petrol

$= p\times \frac{( 100-10)}{10} =0.9\ p$

New volume of petrol with reduced price $= \frac{180}{0.9 p}$   gallons.

As given - a motorist to buy 5 gallons more for rupees 180.

$\frac{180}{0.9p} -\frac{180}{p} =5$

$\frac{(180-180\times0.9)}{0.9p} =5$

$\frac{[180( 1- 0.9)]}{0.9p} =5$

$\frac{180 \times0.01}{0.9p} =5$

$\frac{18}{0.9p} =5$

$p=\frac{18}{5\times 0.9}$

$p= \frac{18}{4.5}$

$p= 4 \ Rs.$

Thus, original price of petrol is  Rs.4 per gallon.