The total cost of a certain length of cloth is 200.If the piece was 5 meter longer and each meter of cloth costs 2 less the cost of the piece would have remain unchanged.How long is the piece and what is the rate per meter?
Answers
Answer:
Step-by-step explanation:
Solution :-
Let the length of cloth be x cm.
Then, cost per metre = Rs. 200/x
Again, new length of the cloth = (x + 5) m
Then, new cost per metre = Rs. (200/x - 2)
According to the Question,
⇒ (x + 5) [(200/x) - 2] = 200
⇒ (x + 5)(200 - 2x)/x = 200
⇒ 200x - 2x² + 1000 - 10x = 200x
⇒ x² + 5x - 500 = 0
⇒ x² + 25x - 20x - 500 = 0
⇒ x(x + 25) - 20(x + 25) = 0
⇒ (x + 25) (x - 20) = 0
⇒ x = - 25, 20 (As x can't be negative)
⇒ x = 20
Hence, Length of the piece is 20 m.
Original cost per metre = 200/20 = Rs. 10
Hence, the Original cost per metre is Rs. 10.
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