A piece of cloth costs Rs. 35. If the piece were 4 m longer and each metre costs Rs. 1 less, the cost would remain unchanged. How long is the piece?
Answers
The piece of the cloth is 10 m long.
• Let the length of the cloth be l m.
• Given,
Price of the cloth piece = Rs. 35
∴ Cost of l m of cloth = Rs. 35
=> Cost of 1 m of cloth = Rs. 35 / l
• If the length of the cloth is increased by 4 m, the new length becomes (l + 4) m.
• Reduced price of each m of cloth piece = (Rs. 35 / l) - 1
= (Rs. 35 - l) / l
• ∴ New cost of the entire cloth piece = New length of cloth × Reduced price per m
= (l + 4) × { (Rs. 35 - l) / l }
= Rs. (l.35 - l.l + 4.35 - 4.l) / l
= Rs. (35l - l² + 140 - 4l) / l
= Rs. (35l - 4l - l² + 140) / l
= Rs. (31l - l² + 140) / l
• It is given that the price of the cloth piece remains unchanged.
∴ According to the question,
Rs. (31l - l² + 140) / l = Rs. 35
=> 31l - l² + 140 = 35 × l
=> 31l - l² + 140 = 35l
=> l² - 31 l + 35l - 140 = 0
=> l² + 4l - 140 = 0
• Now, l² + 4l - 140 = 0 is in the form of a quadratic equation.
∴ l² + 4l - 140 = 0
=> l² + 14l - 10l - 140 = 0
=> l (l + 14) - 10 (l + 14) = 0
=> (l - 10) (l + 14) = 0
=> l - 10 = 0, l + 14 = 0
=> l = 10, l = - 14
• The length of a cloth cannot be negative, therefore, l = - 14 is discarded.
∴ The length of the cloth piece = 10 m