Question

A piece of cloth costs ₹200.if the piece was 5m longer and each metre of cloth costs ₹2 less , the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per metre?

Answer 1

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

x2 +25x -20x -500 =0

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

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

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

so, y = 200/x = 200/20

= 10 Rs....ans.... :)