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A jewellery shop owner conduct his business in the following manner every once in a while he raises his price by a certain percentage and a while later he reduces his prices by the same percentage. after one such uptown cycle of increasing and then decreasing his price by x%, the price of a gewel decreases by 100 rupees. In the next cycle, he increases and then decreases his price by (x/2)% and then sells the Jewel for rupees 2376. What is the initial price of Jewel (in rupees)?
Most Upvoted Answer
A jewellery shop owner conduct his business in the following manner ev...
Solution:
Let the initial price of the Jewel be P.
First Cycle:
- Price increase by x%: P + (x/100)P
- Price decrease by x%: (P + (x/100)P) - (x/100)(P + (x/100)P) = (1 - x/100)(P + (x/100)P)
- After one cycle, the price decreased by 100 rupees: (1 - x/100)(P + (x/100)P) - 100 = P
Solving the above equation for P, we get:
P = [(1 + x/100)/(1 - x/100)] * [(x/100)P + 100]
Second Cycle:
- Price increase by (x/2)%: [(1 + x/200) * P] - P = (x/200)P
- Price decrease by (x/2)%: [(1 + x/200) * P] - [(x/200) * (1 + x/200) * P] = [(1 - x^2/40000) * P]
- After second cycle, the price is 2376: [(1 - x^2/40000) * P] = 2376
Solving the above equation for P using the value of P obtained earlier, we get:
x = 20%
Therefore, the initial price of the Jewel (P) is:
P = [(1 + x/100)/(1 - x/100)] * [(x/100)P + 100] = 2500 rupees.
Let the initial price of the Jewel be P.
First Cycle:
- Price increase by x%: P + (x/100)P
- Price decrease by x%: (P + (x/100)P) - (x/100)(P + (x/100)P) = (1 - x/100)(P + (x/100)P)
- After one cycle, the price decreased by 100 rupees: (1 - x/100)(P + (x/100)P) - 100 = P
Solving the above equation for P, we get:
P = [(1 + x/100)/(1 - x/100)] * [(x/100)P + 100]
Second Cycle:
- Price increase by (x/2)%: [(1 + x/200) * P] - P = (x/200)P
- Price decrease by (x/2)%: [(1 + x/200) * P] - [(x/200) * (1 + x/200) * P] = [(1 - x^2/40000) * P]
- After second cycle, the price is 2376: [(1 - x^2/40000) * P] = 2376
Solving the above equation for P using the value of P obtained earlier, we get:
x = 20%
Therefore, the initial price of the Jewel (P) is:
P = [(1 + x/100)/(1 - x/100)] * [(x/100)P + 100] = 2500 rupees.
Community Answer
A jewellery shop owner conduct his business in the following manner ev...
Say initial price is 100 and he increases by 20%. total 120. Then decreases by 20. Total 120-24=96. Now, Diff here is 4 and in question it is 100,so Multiply by 25. the price would be 2500 and x=20. Now further x/2 also satisfies the condition.
Answer would be 2500
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A jewellery shop owner conduct his business in the following manner every once in a while he raises his price by a certain percentage and a while later he reduces his prices by the same percentage. after one such uptown cycle of increasing and then decreasing his price by x%, the price of a gewel decreases by 100 rupees. In the next cycle, he increases and then decreases his price by (x/2)% and then sells the Jewel for rupees 2376. What is the initial price of Jewel (in rupees)?
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