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.
A) 48
B) 52
C) 64
D) 98

Answer 1

Hint: First convert the given length of wire in cm then find the greatest common divisor of these two numbers which represents the length of the wires. G.C.D of these two numbers is the required answer. We consider G.C.D because it is the greatest among the given and so if we consider it in the length of wires, so the obtained G.C.D will be of greatest among both.

Complete step by step solution: Given:
Length of the long aluminium wire is 9m60cm \[ = 960\]cm
Length of the long copper wire is 5m12cm \[ = 512\]cm
As, we require the maximum length that can be equally cut from each wire in such a way that the total length of each wire is divisible by a factor so, we take the largest common factor or the GCD of the lengths of the 2 wires.
So, G.C.D of \[\left( {960,512} \right)\]
\[960 = {2^6} \times 3 \times 5\]
\[512 = {2^9}\]
So, common factor is \[{2^6}\]= 64
G.C.D of \[\left( {960,512} \right)\]= \[{2^6}\]= 64
Thus, the maximum length that can be equally cut from each wire in such a way that the total length of each wire is exactly is 64.

Hence, option C $=64$ is the correct answer.

Note: Greatest common divisor is the largest positive integer that divides each of the integers. Here in the above question, we have to calculate maximum length therefore we calculate G.C.D of the length of both the wires which will lead to the required solution. As subtracting G.C.D will be left us with 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.