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The price of a product increases by 38% in the first year and then decreases by 20% in the second year. If the initial price of the product is ₹5,100, calculate the final price at the end of the second year.
₹5,490.60
₹5,570.20
₹5,720.80
₹5,630.40
₹5,490.60
Calculate the effective percentage change: 38−20−10038×20=18−7.6=10.4%. Then, 5100×1.104=5630.4.
Initial price = ₹5,100. First-year increase = 38%. Second-year decrease = 20%.
Final Price=P×(1+100R1)×(1−100R2)
Calculate the effective percentage change: 38−20−10038×20=18−7.6=10.4%. Then, 5100×1.104=5630.4.
Many students mistakenly add and subtract percentages directly (38−20=18%) instead of applying the successive percentage change formula.
Calculate price after first year
The price increases by 38%, so multiply the initial price by 1.38.
5100×1.38=7038
Calculate price after second year
The price decreases by 20% from the first-year end price, so multiply by 0.80.
7038×0.80=5630.40
Verify result
The final value calculated is ₹5,630.40, which matches option D.
5630.40
D is correct because the final price after the 38% increase and 20% decrease is ₹5,630.40.
This concept of successive changes is identical to calculating Compound Interest where the rates differ annually.