Question

A piece of iron rod costs rs 60 if the rod was 2 meter shorter and each meter costs rs 1more the cost would remain unchanged..What's the length of the rod

Answer 1

Answer:  The required length of the rod is 12 meters.

Step-by-step explanation:  Given that a piece of iron rod costs rs 60 if the rod was 2 meter shorter and each meter costs Rs. 1 more, the cost would remain unchanged.

We are to find the length of the rod.

Let x meter represents the length of the rod and Rs. c represents the cost of the rod per meter.

Then, according to the given information, we have

$xc=60~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$(x-2)(c+1)=60\\\\\Rightarrow xc-2c+x-2=60\\\\\Rightarrow 60-2\times\dfrac{60}{x}+x-2=60~~~~~~~~~~~~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\\\Rightarrow x-\dfrac{120}{x}-2=0\\\\\Rightarrow x^2-120-2x=0\\\\\Rightarrow x^2-12x+10x-120=0\\\\\Rightarrow x(x-12)+10(x-12)=0\\\\\Rightarrow (x-12)(x+10)=0\\\\\Rightarrow x-12=0,~~~x+10=0\\\\\Rightarrow x=12,-10.$

Since x is the length of the rod, so it cannot be negative.

Thus, the required length of the rod is 12 meters.