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प्रश्न
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. 1 less, the cost would remain unchanged. How long is the piece?
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उत्तर
Let the length of the piece be x metres.
Then, rate per metre = `35/x`
According to question, new length = (x + 4) meters.
Since the cost remain same. Therefore, new rate per metre `=35/(x+4)`
It is given that
`35/x+35/(x+4)=1`
`(35(x+4)-35x)/(x(x+4))=1`
`(35x+140-35x)/(x^2+4x)=1`
`140/(x^2+4x)=1`
140 = x2 + 4x
x2 + 4x − 140 = 0
x2 + 14x − 10x − 140 = 0
x(x + 14) − 10(x + 14) = 0
(x + 14) (x − 10) = 0
x + 14 = 0
x = −14
Or
x − 10 = 0
x = 10
Because x cannot be negative.
Thus, x = 10 is the require solution.
Therefore, the length of the piece be x = 10 meters.
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