Given:
The price of fuel decreases by 30%, 20%, and 10% in three successive months and increases by 65% in the fourth month.
Formula used:
To calculate the successive percentage change in price, the formula is:
New Price = Initial Price × (1 + Percentage Change 1) × (1 + Percentage Change 2) × (1 + Percentage Change 3) × (1 + Percentage Change 4)
Percentage Change = ((Final Price - Initial Price) / Initial Price) × 100
Calculations:
Assume the original price of fuel is ₹100 for simplicity.
1st Month Price: ₹100 × (1 - 30/100) = ₹100 × 0.7 = ₹70
2nd Month Price: ₹70 × (1 - 20/100) = ₹70 × 0.8 = ₹56
3rd Month Price: ₹56 × (1 - 10/100) = ₹56 × 0.9 = ₹50.4
4th Month Price: ₹50.4 × (1 + 65/100) = ₹50.4 × 1.65 = ₹83.16
Percentage Change in Price as compared to its original price:
⇒ Percentage Change = ((₹83.16 - ₹100) / ₹100) × 100
⇒ Percentage Change = (₹83.16 - ₹100) / ₹100 × 100
⇒ Percentage Change = -16.84%
∴ The correct answer is option 4 (Decreases by 16.84%).