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In the Garbar Jhala, Aminabad a shopkeeper first raises the price of a Jewellery by x% then he decreases the new price by x%. After one such up-down cycle, the price of a Jewellery decreased by Rs. 21025. After a second up-down cycle, the jewellery was sold for Rs. 484416. What was the original price of the jewellery?

A
Rs. 5,00,000
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B
Rs. 6,00,625
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C
Rs. 525625
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D
Rs. 5,26,000
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Solution

The correct option is A Rs. 525625
Let the original price be p, then the decrease in value of p after one cycle.
=p(x100)2=21025(i)
Again the final value after second cycle
p(1+x100)(1x100)(1+x100)(1x100)=484416p[1(x100)2]2=484416(ii)
Dividing equation (ii) by equation (i)
[1(x100)2]2(x100)2=48441621025=2304100 1(x100)2(x100)=2304100=4810
Let x100=k, then
1k2k=481010k2+48k10=05k224x5=0k=5 or k=15(inadmissible value)So,x=20%Hence,p(x100)2=21025p=525625

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