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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? - Mathematics

MCQ

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

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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"`

Concept: Arithmatic (Entrance Exam)
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