Calculating Fuel Price Percentage Change

To find the net percentage change in the fuel price after successive monthly changes, we can track the price changes step by step. Let's assume the original price of the fuel is $100$ units.

Step 1: Price After First Month Decrease

The price decreases by $30\%$. The new price is:

Price = $100 \times (1 - \frac{30}{100}) = 100 \times (1 - 0.30) = 100 \times 0.70 = 70$ units.

Step 2: Price After Second Month Decrease

The price further decreases by $20\%$. The price becomes:

Price = $70 \times (1 - \frac{20}{100}) = 70 \times (1 - 0.20) = 70 \times 0.80 = 56$ units.

Step 3: Price After Third Month Decrease

The price decreases again by $50\%$. The price is now:

Price = $56 \times (1 - \frac{50}{100}) = 56 \times (1 - 0.50) = 56 \times 0.50 = 28$ units.

Step 4: Price After Fourth Month Increase

In the fourth month, the price increases by $40\%$. The final price is:

Price = $28 \times (1 + \frac{40}{100}) = 28 \times (1 + 0.40) = 28 \times 1.40 = 39.2$ units.

Step 5: Calculate Overall Percentage Change

The original price was $100$ units, and the final price is $39.2$ units.

Change in price = Final Price - Original Price = $39.2 - 100 = -60.8$ units.

The overall percentage change is:

Percentage Change = $ \frac{\text{Change in Price}}{\text{Original Price}} \times 100 = \frac{-60.8}{100} \times 100 = -60.8\%$

A negative percentage change indicates a decrease.

Conclusion

The price of fuel shows a net decrease of $60.8\%$ compared to its original price.