If a shopkeeper first raises the price of jewelry by x% then he decreases the…
2024
If a shopkeeper first raises the price of jewelry by x% then he decreases the new price by x%. After one such up down cycle, the price of a jewelry decreased by Rs. 1200. After a second up down cycle the jewelry was sold for Rs. 27648. What was the original price of the jewelry ?
- A.
Rs. 24000
- B.
Rs. 36000
- C.
Rs. 44000
- D.
Rs. 30000
Attempted by 36 students.
Show answer & explanation
Correct answer: D
Solution:
Let the original price be P and let x% = x/100 = r.
One up-down cycle multiplies the price by (1 + r)(1 - r) = 1 - r^2, so the drop after one cycle is P - P(1 - r^2) = Pr^2 = 1200.
Hence r^2 = 1200 / P. After two cycles the price becomes P(1 - r^2)^2 = 27648.
Substitute r^2 to get: P(1 - 1200/P)^2 = 27648, which simplifies to (P - 1200)^2 = 27648·P.
Expand and rearrange: P^2 - 30048P + 1,440,000 = 0. This factors as (P - 30000)(P - 48) = 0.
P = 30000 or P = 48. Since the drop after one cycle is 1200, the original price must exceed 1200, so P = 30000.
Optional check: r^2 = 1200/30000 = 0.04 so r = 0.2 (x = 20%). After two cycles price = 30000·(0.96)^2 = 27648, which matches the given value.
Answer: Rs. 30000