Question

A certain piece of cloth costs 7200. If the piece was 5m long and each
meter of cloth cost was 32 less, the cost of the piece would have remained
unchanged. How long is the piece and what is the original rate per meter?​

Answer 1

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)=200

or, xy+5y-2x-10=200

or, 200+5y-2x-10=200

or, 5y-2x-10=0

or, 5y=2x+10

or, y=(2x+10)/5

Putting in (1),

x(2x+10)/5=200

or, x(2x+10)=200×5

or, 2x²+10x=1000

or, x²+5x-500=0

or, x²+25x-20x-500=0

or, x(x+25)-20(x+25)=0

or, (x+25)(x-20)=0

either, x+25=0

or, x=-25

or, x-20=0

or, x=20

Since the length of the cloth can not be negative,

∴, x=20 metre

Putting in (1),

20y=200

or, y=10

∴, the cloth is 20 m long and the original rate is Rs. 10/metre. Ans.