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ஒரு பொருளின் விலை ₹1600. இது முதல் ஆண்டில் 10% மற்றும் இரண்டாம் ஆண்டில் 30% அதிகரித்தது. இரண்டு ஆண்டுகளுக்குப் பிறகு அந்தப் பொருளின் விலை (₹ இல்) என்ன?
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.