The total cost of a certain length of cloth os 200rupee if the piece was 5m longer and each metre of cloth costs rupee 2 less the cost pf the piece would remain unchanged what is the length of the original piece of cloth and cost per metre
Answers
let cost of per meter = Rs x
let length of cloth = y meters
⇒ x × y = Rs 200 [ total cost ]
⇒ x = 200/y ------------------- eq 1
condition 2
if piece is 5m longer that is new length = (y + 5 )m and
cost per meter is Rs 2 less that is (x-2) , no change is total cost
⇒ (x-2) (y + 5 ) = 200 ------------------- eq 2
substituting value of x from eq 1 in eq 2 we get
⇒ ((200/y)-2) (y + 5 ) = 200
⇒ (200 -2y)(y+5) = 200y
⇒ 200y + 1000 - 2y² -10 y = 200y
⇒ 2y² +10y - 1000 = 0
⇒ y² + 5y - 500 = 0
⇒ y² + 25y - 20y - 500 = 0
⇒ y(y + 25) - 20( y + 25 ) = 0
⇒ (y - 20) ( y + 25 ) = 0
⇒ y = 20 or y = -25
ignoring the negative value length can't be negative
y = 20 meters
cost x = 200/y [ from equation 1 ]
cost = 200/20 = rs 10 per meter
hence length of original piece = 20 meters
cost per meter = Rs 10