A piece of cloth costs rupees 75 If the piece is four meters longer and each meter costs rupees 5 le...........

Quantitative Aptitiude (CLAT) Number System

A piece of cloth costs rupees 75. If the piece is four meters longer and each meter costs rupees 5 less, the cost remains unchanged. What is the length of the piece?

8 meters

10 meters

12 meters

6 meters

Explanation:

Let price per m = RS y
let the piece of cloth = x metres
given that,
Total cost = RS 75
xy = 75
y = 75/x ( result 1)
ALSO given that
if the piece of cloth is 4 metres long and cost per metre is 5 rs less..the cost remains unchanged
=) (x+4)(y-5) =75
xy-5x+4y-20=75
xy-5x+4y-95=0
x(75/x)-5x+4(75/x)-95=0. (from result 1)
75 -5x +(300/x )-95=0
after futher simplification
-5x²-20x+300=0
x²+4x-60=0
x²+(10-6)x-60=0
(x+10)(x-6)=0
(x+10)=0
x= -10 (INVALID AS MEASUREMENTS CANNOT BE NEGATIVE)
(x-6)=0
x=-6
therefore the length of the cloth is 6 metres