Question

a play piece of cloth is rupees 200 if the peace were 5 metres long and 8 metre of cloth cost rupees to less the cost of the price would remain unchanged how long is the peace 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 -2x = 10x
500 -xSq = 5x
xSq +5x - 500 = 0
xSq +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.... :)