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The price of fuel decreases by 50%, 35% and 50% in three successive months, but increases by 45% in the fourth month. What is the percentage increase/
Question

The price of fuel decreases by 50%, 35% and 50% in three successive months, but increases by 45% 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? (Round off the answer to two decimal places)

A.

Decreases by 76.44%

B.

Increases by 81.75%

C.

Increases by 80.11%

D.

Decreases by 74.19%

Correct option is A

Given:
Successive price changes:  −50%,−35%,−50%,+45%-50\%, -35\%, -50\%, +45\%​​
Formula Used:
Final Value = Initial Value ×(1±Change%100)× (1 \pm \frac{Change \%}{100})​​
Solution:
Let the original price be 100.
Price after 1st month = 100×(1−50100)=50100 × (1 - \frac{50}{100}) = 50​​

Price after 2nd month = 50×(1−35100)=50×0.65=32.550 × (1 - \frac{35}{100}) = 50 × 0.65 = 32.5​​

Price after 3rd month = 32.5×(1−50100)=32.5×0.50=16.2532.5 × (1 - \frac{50}{100}) = 32.5 × 0.50 = 16.25​​

Price after 4th month = 16.25×(1+45100)=16.25×1.45=23.5625 16.25 × (1 + \frac{45}{100}) = 16.25 × 1.45 = 23.5625​​
Change in price = Initial Price - Final Price
Change = 100 - 23.5625 = 76.4375%
Rounding off to two decimal places gives a decrease of 76.44%
Final Answer
So the correct answer is (a) 

Exam Hall Method: ​

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