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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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একটি পণ্যের দাম প্রথম বছরে 38% বৃদ্ধি পায় এবং দ্বিতীয় বছরে 20% হ্রাস পায়। যদি পণ্যের প্রাথমিক মূল্য 5,100 টাকা হয়, তাহলে দ্বিতীয় বছরের শেষে চূড়ান্ত মূল্য নির্ণয় করুন।
5,490.60 টাকা
5,570.20 টাকা
5,720.80 টাকা
5,630.40 টাকা
5,490.60 টাকা
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.