Question:
A piece of cloth costs Rs. 35. If the piece were 4m longer and each meter costs Rs. One less, the cost would remain unchanged. How long is the piece
Answer:
Let the length of the cloth = x meter
Now, cost of 1 m cloth = 35/x
According to question,
35/x - 1 = 35/(x + 4)
=> 35/x - 35/(x + 4) = 1
=> {35(x + 4) - 35x}/{x*(x + 4)} = 1
=> 35(x + 4) - 35x = x*(x + 4)
=> 35x + 140 - 35x = x2 + 4x
=> x2 + 4x = 140
=> x2 + 4x - 140 = 0
=> (x + 14)*(x - 10) = 0
=> x = 10, -14
Since Length can not be negative,
So, x = 10
Hense, the length of piece is 10 m
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