Question

A piece of cloth cost rs.35.if the piece were 4m longer and each meter cost rs.1.the cost would remain unchanged.how long is the piece?

Answer 1

$let \: length \: of \: cloth = x \\ cost \: of \: 1m = y \\ xy = 35 \\ if \: length \: = x + 4 \\ cost \: = y - 1 \\ (x + 4)(y - 1) = 35 \\ xy + 4y - x - 4 = 35 \\ 35 + 4y - x - 4 = 35 \\ 4y - x - 4 = 0 \\ 4 \frac{35}{x} - x - 4 = 0 \\ 140 - {x }^{2} - 4x = 0 \\ {x}^{2} + 4x - 140 = 0 \\ {x }^{2} + 14x - 10x - 140 = 0 \\ x(x + 14) - 10(x + 14) = 0 \\ (x + 14)(x - 10) = 0 \\ x = 10 \\ length \: of \: cloth = 10 \\ cost \: of \: 1m = rs \: 3.5$

Answer 2

SOLUTION :  

Let the length of the piece of  cloth be x metres.

Then , Rate per meter = 35/x

New length of the piece of  cloth be (x + 4)  

New Rate per meter = 35/(x + 4)

[Cost remain same ]

A.T.Q

35/x - 1 = 35/(x + 4)

35/x - 35/(x + 4) = 1

[35(x + 4) - 35x] / [x(x + 4)] = 1

[By taking LCM]  

35(x + 4) - 35x = x(x + 4)

35x + 140 - 35x = x² + 4x

x² + 4x - 35x - 35x - 140 = 0

x² + 4x - 140 = 0

x² + 14x - 10x - 140 = 0

[By middle term splitting]

x(x + 14) - 10(x + 14) = 0

(x + 14) (x - 10) = 0

(x + 14) = 0  or (x - 10) = 0

x = - 14  or x = 10

Since, length can't be negative,so x ≠ - 14

Therefore , x = 10

Hence, the length of piece of cloth is 10 m.

HOPE THIS ANSWER WILL HELP YOU….