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Examoogle • User • info@examoogle.com • EE-2024-8821
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एका वस्तूची किंमत ₹1600 होती. पहिल्या वर्षी ती 10% ने आणि दुसऱ्या वर्षी 30% ने वाढली. दोन वर्षांनंतर वस्तूची किंमत (₹ मध्ये) किती आहे?
2080
2288
1760
2248
2288
Use the formula: Final=P×1.1×1.3. Effectively, 1600×1.43=2288.
Initial price of the article = ₹1600. First-year increase = 10%. Second-year increase = 30%.
Final Price=InitialPrice×(1+100r1)×(1+100r2)
Use the formula: Final=P×1.1×1.3. Effectively, 1600×1.43=2288.
Many students calculate simple interest by adding 10% and 30% to get 40% (₹640) and adding it to the original, ignoring the compounding effect of the second-year increase on the already increased first-year price.
Calculate price after the first year
Apply the 10% increase to the initial price: 1600+(10% of 1600)=1600+160=1760.
1600×1.1=1760
Calculate price after the second year
Apply the 30% increase to the new price of ₹1760: 1760+(30% of 1760)=1760+528.
1760×1.3=2288
Final Verification
Combining the multipliers: 1600×1.1×1.3=1600×1.43=2288.
1600×(100110)×(100130)=2288
B is correct because the price after two years of successive increases is ₹2288.
This concept of successive percentage change is identical to calculating Compound Interest over two periods or successive discounts.