A piece of cloth costs Rs.35. If the piece were 4m longer and each meter were to cost Rs.1 lesser,then the total cost would remain unchanged. Find the length of the piece of cloth ?
If the length is x and the cost is c, then
xc = 35
(x+4)(c-1) = 35
(x+4)(35/x - 1) = 35
solve to get x = 10
check: 10*3.5 = 14*2.5 = 35
To find the length of the piece of cloth, let's assume the original length is 'x' meters.
According to the given information, the cost of the cloth is Rs. 35 and the new length is 4 meters longer. Therefore, the new length would be (x + 4) meters.
If each meter costs Rs. 1 lesser, the new cost per meter would be (Rs. 35 - Rs. 1) = Rs. 34.
We know that the total cost remains unchanged, so we can set up the equation:
Original cost = New cost
Original cost per meter * Original length = New cost per meter * New length
Rs. 35 * x = Rs. 34 * (x + 4)
Now, let's simplify the equation to solve for 'x':
35x = 34(x + 4)
35x = 34x + 136
35x - 34x = 136
x = 136
Therefore, the length of the piece of cloth is 136 meters.