Question

A piece of cloth cost 35 if the piece were 4m longer each meter were to cost 1 rupee lesser, than the total cost would be unchanged. How many meters the cloth
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Answer 1

Answer:

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.

Step-by-step explanation:

Answer 2

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

Then , Rate per meter = 35/4

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.