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Q1.A shopkeeper buys a number of pens for Rs80.If he had bought 4 more pens for the same amount , each pen would have cost him Rs 1 less. How many pens did

Let the no of pens=x Total cost of the pens=Rs.80 ⇒cost of each pen=Rs.80/x If the no of pens is(x+4),then the cost of each pen is Rs 80/(x-4) 80/x-80/(x+4)=1 ⇒80(x+4)-80x/x(x+4)=1-[Taking LCM] ⇒80x+320-80x=x(x+4) ⇒320=x²+4x-[cancel 80x] ⇒x²+4x-320=0 ⇒x²+20x -16x-320=0 ⇒ By grouping, ⇒x(x+20)-16(x+20)=0 ⇒(x+20)(x-16)=0 ⇒(x+20)=0 or (x-16)=0 ⇒x=-20 or x=16 Therefore,Number of pens=x=Rs.16 Number of pens cannot be negative Hence,-20 is rejected Therefore, cost of each pen=80/x=80/16 =Rs.5