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Question
The value of an article decreases for two years at the rate of 10% per year and then in the third year it increases by 10%. Find the original value of the article, if its value at the end of 3 years is Rs. 40,095.
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Solution
Let X be the value of the article.
The value of an article decreases for two years at the rate of 10% per year.
The value of the article at the end of the 1st year is
X - 10% of X = 0.90X
The value of the article at the end of the 2nd year is
0.90X - 10% of (0.90X) = 0.81X
The value of the article increases in the 3rd year by 10%.
The value of the article at the end of 3rd year is
0.81x + 10% of (0.81x) = 0.891x
The value of the article at the end of 3 years is Rs. 40,095.
0.891X = 40,095
⇒ X = 45,000
The original value of the article is Rs. 45,000.
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