The price of fuel decreases by 55%, 55% and 30% 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? [Give your answer correct to two places after decimal.]

The correct option is Decreases by 78.74%.

Let the original price of fuel be $P$. We will calculate the price of fuel after each of the four months step-by-step.

Step 1: First Month Decrease (55% decrease)
A decrease of 55% means the new price is 45% (100% - 55%) of the original price.
Price after Month 1 = $P\times 0.45$

Step 2: Second Month Decrease (55% decrease)
The price decreases by 55% again from its value at the end of Month 1.
Price after Month 2 = $(P\times 0.45)\times 0.45=P\times 0.2025$

Step 3: Third Month Decrease (30% decrease)
A decrease of 30% means the new price is 70% (100% - 30%) of the price at the end of Month 2.
Price after Month 3 = $(P\times 0.2025)\times 0.70=P\times 0.14175$

Step 4: Fourth Month Increase (50% increase)
An increase of 50% means the new price is 150% (100% + 50%) of the price at the end of Month 3.
Price after Month 4 = $(P\times 0.14175)\times 1.50=P\times 0.212625$

Step 5: Determine the Net Percentage Change
The final price in the fourth month is 0.212625 times the original price $P$. To find the percentage change, we subtract this factor from 1:
Net Change = $1-0.212625=0.787375$

Converting this to a percentage:
Net Percentage Decrease = $0.787375\times 100\%=78.7375\%$

Rounding to two decimal places, the price of fuel decreases by 78.74% compared to its original price.