# THE TOTAL COST OF A CERTAIN LENGTH OF A PIECE OF CLOTH IS RS 200.IF THE PIECE WAS 5 METRE LONGER AND EACH METRE OF CLOTH COSTS RS 2 LESS .THE COST OF THE PIECE WOULD HAVE REMAINED UNCHANGED .HOW LONG IS THE PIECE AND WHAT IS ITS ORIGINAL RATE PER METRE.

1
by ashboshandiana

2016-03-17T09:13:57+05:30
Let the length of the original piece be x
Now, its price = Rs.200

Price per m = 200/x --Eq.1

Now, if the cloth was 5 m longer, its length = x+5
and
Price per m would be 200/x+5 --Eq.2
(As total price is unchanged)
Or
Price per m would be Rs.2 less than the original one i.e.
200/x -2 -- Eq.3

Equating Eq.2 and Eq.3,

200/x+5 = 200/x - 2
200/x+5 = 200-2x/x
200x/x+5 = 200 -2x
200x = (x+5)(200-2x)
200x = 200x -2x² +1000 -10x
Cut 200x from both sides
-2x² +190x +1000 = 0

Substituting values in the formula.

Root 1 = 10 +√[10² - 4(-2)(1000)]/ -4
= 10+90/-4
= 100/-4
= -25

Root 2 = 10 -√[10² - 4(-2)(1000)]/ -4
= 10- 90/-4
= -80/-4
= 20

Now, the length of the original piece cannot be negative.

So, the length of original piece is 20 m.(Root 2)
And original rate = 200/x = 200/20 = Rs.10