Question

There are two electrical wires one is a $9m60cm$ long aluminium wire and the other is $5m12cm$ long copper wire. Find the maximum length that can be equally cut from each wire in such a way that the total length of each wire is exactly divisible by it.

• A. $48$
• B. $52$
• C. $64$
• D. $98$

Answer 1

The correct option is C $64$

The given two wires are $9m60cm$ and $5m12cm$ long. We know that $1m=100$cm, therefore,

The length of the respective wires will be:

Aluminium wire $=9\times 100+60=900+60=960$cm

Copper wire $=(5\times 100)+12=500+12=512$cm

Now, let us factorize the length of the wires as follows:

$960=2\times 2\times 2\times 2\times 2\times 2\times 3\times 5512=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

The highest common factor (HCF) is $2\times 2\times 2\times 2\times 2\times 2=64$

Hence, the maximum length that can be equally cut from each wire in such a way that the total length of each wire is exactly divisible by it is $64$cm.