a piece of cloth cost Rs 35 if the length of the piece would have been 4 meter

Question

a piece of cloth cost Rs 35 if the length of the piece would have been 4 meter longer and each meter costs rs 1 less the cost would have remained unchanged how long is the price 

 

can anybody explain in detail

Answer 1

Cost of L = 35

So cost per m =35/L

 

Cost for( L+4 m ) is  (35/L ) - 1 per m

so the total cost = (35/L -1 ) x ( L + 4) is also 35

 

(35 -L)( L + 4) =35 L

 

35L -L² -4L + 35x4 =35L 

 

-L² -4L + 140 =0

 

L² +4L -140 =0 

 

Solving this quadratic equation gives L = -14 m and 10 m 

Answer is 10m @ 3.5 per m and 14 m @ 2.5 per m the cost will be Rs 35 in each case