Question

A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. one less, the cost would remain unchanged. How long is the piece?

Answer 1

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….

Answer 2

$Here \ Is \ answer$

A piece of cloth cost Is Rs. 35.

the piece were 4 m longer and each meter costs Rs less, the cost would remain unchanged.

So,

Let the length of the cloth = x meter

Now, Take the cost of 1 m cloth = 35/x

According to the Question,

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

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

=> {35(x + 4) - 35x}/{x*(x + 4)} = 1

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

=> 35x + 140 - 35x = x2 + 4x

=> x2 + 4x = 140

=> x2 + 4x - 140 = 0

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

=> x = 10, -14

But, lenth cannot be negative,

So, x = 10

So, The lenght of price is 10 meter .

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