The price of fuel decreases by 35%, 10% and 30% in three successive months, but increases by 65% 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?

Given:

Initial price of fuel = 100 (assume for calculation)

Decrease in price for 1^st month = 35%

Decrease in price for 2^nd month = 10%

Decrease in price for 3^rd month = 30%

Increase in price for 4^th month = 65%

Formula used:

Successive percentage change formula:

Price after percentage decrease = Initial Price × \((1 - \frac{\text{percentage decrease}}{100})\)

Price after percentage increase = Initial Price × \((1 + \frac{\text{percentage increase}}{100})\)

Overall percentage change = \(\frac{\text{Final Price} - \text{Initial Price}}{\text{Initial Price}} \times 100\)

Calculations:

Price after 1^st month:

⇒ 100 × \((1 - \frac{35}{100}) \) = 100 × 0.65 = 65

Price after 2^nd month:

⇒ 65 × \((1 - \frac{10}{100})\)  = 65 × 0.90 = 58.5

Price after 3^rd month:

⇒ 58.5 × \((1 - \frac{30}{100}) \) = 58.5 × 0.70 = 40.95

Price after 4^th month:

⇒ 40.95 × \((1 + \frac{65}{100}) \) = 40.95 × 1.65 = 67.5675

Overall percentage change:

⇒ \(\frac{67.5675 - 100}{100} × 100 = \frac{-32.4325}{100} × 100 \) = -32.43%

∴ The correct answer is option (2): Decreases by 32.43%.