The price of fuel decreases by 20%, 35% and 20% in three successive months, but increases by 50% in the fourth month. What is the percentage increase/decrease in the price of fuel in the fourth month as compared to its original price?

Correct option is A

Given:

The price of fuel decreases by 20%, 35%, and 20% in three successive months.

The price increases by 50% in the fourth month.

We need to find the percentage change in the price of fuel in the fourth month compared to its original price.

Formula Used:

Percentage change = $$\left( \frac{\text{Final price}}{\text{Original price}} - 1 \right) \times 100$$​​

Solution:  ​

Let the initial Price be 100 

Final price = $$100 \times (1 - \frac{20}{100}) \times (1 - \frac{35}{100}) \times (1 - \frac{20}{100}) \times (1 + \frac{50}{100})$$

​$$=100 \times (\frac{80}{100}) \times ( \frac{65}{100}) \times ( \frac{80}{100}) \times ( \frac{150}{100}) \\ \ \\ = 62.4$$​

Percentage change = $$\left( \frac{62.4}{100}-1\right)\times100 =-37.6\%$$​​

Thus, the overall percentage change in the price of fuel after the four months is a decrease of 37.6% compared to its original price.