Explanation:

This problem can be solved by either the conventional method or by using the answer options.
After the first cycle, the value of the article decreased by Rs. 1,000.
∴ The original price has to be more than Rs. 23,040
Hence, options 1 and 2 can be eliminated.
x% increase and x% decrease is equivalent to (1 + x/100) (1 - x/100)
∴ Old price × [1 - x²/10000] = New price
∴ Old price − new price = old price × [x² /10000]
i.e. 1000 = old price × [x² /10000]
Consider option C: Old price = 25000
∴ 1000 = 25000 × [x² /10000]
∴    x² = 400   i.e. x = 20%
∴  Change for second year = (1 + 0.2)(1 − 0.2) = (1.2)(0.8) = 0.96
Observe that value of old price : new price for second year = 23040 : 24000 = 0.96
Hence, original price of article = Rs. 25,000