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Question
A man buys a number of pens for ₹ 180. If he had bought 3 more pens for the same amount, each pen would have cost him ₹ 3 less. How many pens did he buy?
Solution
Let the total number of pens be x.
According to the question:
`80/x-80/(x+4)=1`
⇒`(80(x+4)-80x)/((x(x+4) `=1
⇒`320=x^2+4x`
⇒`x^2+4x-320=0`
⇒`x^2+(20-16)x-320=0`
⇒`x^2+20x-16x-320=0`
⇒`x(x+20)-16(x+20)=0`
⇒`(x+20)(x-16)=0`
⇒`x=-20 or x=16`
The total number of pens cannot be negative; therefore, the total number of pens is 16.
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