A trader purchased some pens for Tk. 150. If the price of each pen was Tk. 5 less, he would have got 5 more pens. How many pens did he buy?

A trader purchased some pens for Tk. 150. If the price of each pen was Tk. 5 less, he would have got 5 more pens. How many pens did he buy? Correct Answer 10

Let the number of pens bought by him be P. Then, the price of each pen = 150/P According to the question, 150/(P + 5) = (150/P) - 5 or,  (P + 5) x {(150/P) - 5} = 150 or, 150 - 5P + 750/P - 25 = 150 or,  (750 - 5P2)/P = 25 or,  750 - 5P2  = 25P or,  5P2  + 25P - 750 = 0 or, P2  + 5P - 150 = 0 or, P2  + 15P - 10P - 150 = 0 or, (P + 15)(P - 10) = 0 So,   P = 10.
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