A company regularly changes price of its laptops according to market demand. In January, they increased the price by X% and decrease it by X% in February. Due to it, the price of the laptop was decreased by Rs. 200 with respect to its price in January. Company did the same thing in March and April, first increasing the price by X% and then decreasing it by X%. The final price after whole cycle was Rs. 19,602. What is the original price of the laptop before January?
Explanation:
For the first increase decrease cycle of +x% and -x%, overall change would be (-x2/100)%. This results in a decrease of 200 and the price becomes P – 200.
The next increase decrease cycle of +x% and -x% would be on a smaller base of (P – 200). The overall change would be the same(-x2/100)%. The absolute change would be (P - 200) × x2/100 which would definitely be less than 200.
Hence, the total change after 2 such cycles would definitely be more than 200 but less than 400. Only option (b) satisfies this criterion.
Alternately,
Let P be the original price of the laptop.
According to the question,
After one cycle, P1+x1001-x100 = P - 200
1+x1001-x100 = P-200P ...(1)
After second cycle, P1+x10021-x1002 = 19,602
From (1)
(P-200)2P = 19602 ...(2)
⇒ (P – 200)2 – 19602P = 0
⇒ P2 – 20002P + 40000 = 0
⇒ P = 20,000 and 2
P = 2 is not possible.
Hence, P = Rs. 20,000
Hence, option (b).
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