a piece of cloth costs rs 200.if the piece were 5m longer and each metre of cloth costed rs 2 less the cost of the piece would have remained unchanged.how long is the piece and what is he original rate per metre?

let the length of the cloth be x and cost of cloth per m be y then,

x * y = 200

so, y = 200/x ....(1)

now, If the piece were 5m longer, and each metre of cloth costed Rs 2 less, then,

(x+5)(y -2) = 200.

xy -2x + 5y -10 = 200

putting the value of (1), we get,

1000/x - 2x = 200 - 190

1000 -2x² = 10x

500 -x² = 5x

x²+5x - 500 = 0

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

so, x= 20 (neglecting x= -25)

so, y = 200/x = 200/20 = 10

Hence, the length of the piece of cloth is 20 m and rate per metre is Rs 10.