Examveda

A shopkeeper first raises the price of Jewellery by x% then he decreases the new price by x%. After 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. 5,26,000

B. Rs. 6,00,625

C. Rs. 5,25,625

D. Rs. 5,00,000

E. None of these

Answer: Option C

Solution(By Examveda Team)

Let the initial price = Rs. 10000p
Price after first increment = 10000p + 100xp
Price after first decrement
= 10000p + 100xp - (100px + px2)
= 10000p - px2
Now, total decrement, px2 = 21025 . . . . . (1)
Price after second increment,
= 10000p - px2 + 100xp - $$\frac{{{\text{p}}{{\text{x}}^3}}}{{100}}$$
Price after second increment,
= 10000p - p2 + 100xp - $$\frac{{{{\text{p}}^3}}}{{100}}$$ - 100xp + $$\frac{{{\text{p}}{{\text{x}}^3}}}{{100}}$$ - px2 + $$\frac{{{\text{p}}{{\text{x}}^4}}}{{10000}}$$
= 10000p - 2px2 + $$\frac{{{\text{p}}{{\text{x}}^2}}}{{10000}}$$
= 484416 . . . . . . (2)
On solving equation (1) and (2), We get
x = 20
Substituting back we get,
p = 5,25,625
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