Q 18: A piece of cloth costs 200. If the piece was 5 m longer and each meter of cloth costed & 2 less,the cost of the price would have remained unchanged. How long is the piece and what is its originalrate per meter?

Q 18: A piece of cloth costs 200. If the piece was 5 m longer and each

1.	Q 18: A piece of cloth costs 200. If the piece was 5 m longer and each meter of cloth costed & 2 less,the cost of the price would have remained unchanged. How long is the piece and what is its originalrate per meter?
Answer» Let the piece of cloth is x metre and it costs Rs.y/metre. Then by the given conditions -∴, xy=200 -------------(1) and(x+5)(y-2)=200or, xy+5y-2x-10=200or, 200+5y-2x-10=200or, 5y-2x-10=0or, 5y=2x+10or, y=(2x+10)/5Putting in (1),x(2x+10)/5=200or, x(2x+10)=200×5or, 2x²+10x=1000or, x²+5x-500=0or, x²+25x-20x-500=0or, x(x+25)-20(x+25)=0or, (x+25)(x-20)=0either, x+25=0or, x=-25or, x-20=0or, x=20Since the length of the cloth can not be negative,∴, x=20 metrePutting in (1),20y=200or, y=10∴, the cloth is 20 m long and the original rate is Rs. 10/metre. Ans.