The price of fuel decreases by 40%, 30% and 10% in three successive months, but increases by 40% 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:
Price of fuel decreases by 40%, 30%, and 10% successively in the first three months.
Price increases by 40% in the fourth month.
Formula Used:
​$$\text{Final Price} = \text{Initial Price} \times \left(1 + \dfrac{p_1}{100}\right) \times \left(1 + \dfrac{p_2}{100}\right) \times \left(1 + \dfrac{p_3}{100}\right) \cdots$$​​
 $$\text{Percentage Change} = \left(\dfrac{\text{Final Price} - \text{Initial Price}}{\text{Initial Price}}\right) \times 100$$​​
Solution:
Let the original price of fuel = 100 units.
​$$\begin{aligned}&\text{After a 40\% decrease:} \\&\quad 100 \times \left(1 - \dfrac{40}{100}\right) = 100 \times 0.6 = 60 \;\; \text{units} \\\\&\text{After a 30\% decrease:} \\&\quad 60 \times \left(1 - \dfrac{30}{100}\right) = 60 \times 0.7 = 42 \;\; \text{units} \\\\&\text{After a 10\% decrease:} \\&\quad 42 \times \left(1 - \dfrac{10}{100}\right) = 42 \times 0.9 = 37.8 \;\; \text{units} \\\\&\text{After a 40\% increase:} \\&\quad 37.8 \times \left(1 + \dfrac{40}{100}\right) = 37.8 \times 1.4 = 52.92 \;\; \text{units}\end{aligned}$$​​
Percentage Change = $$\left(\dfrac{52.92 - 100}{100}\right) \times 100 = -47.08\%$$​​
The price of fuel decreased by 47.08% compared to the original price.