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Question
Choose the most appropriate option
A piece of cloth costs rupees 75. If the piece is four meters longer and each meter costs rupees 5 less, the cost remains unchanged. What is the length of the piece?
Options
10 meters
12 meters
6 meters
8 meters
Solution
6 meters
Explanation:
According to question,
Let the length of a piece of cloth be x
Let the rate per meter be y
∴ x y = 75
`"x"=75/"y"`
Again, 4 meters longer and ₹ 5 less
Then,
(x + 4) (y − 5) = 75
(x + 4) (y − 5) = x y
x y − 5x + 4y − 20 = x y
4 y − 5 x = 20
`4"y"-5xx75/"y"=20`
⇒ 4y2 − 20y −375 = 0
By solving,
we get y = 12.5
Rate per meter = 12.5
Price of cloth = 75
∴ Length of cloth =`75/12.5=6 "meters"`
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