Question

Three ropes are $7m,12m95cm$ and $3m85cm$ long. What is the greatest possible length that can be used to measure these ropes?

• A. $35cm$
• B. $55cm$
• C. $1m$
• D. $65cm$

Answer 1

The correct option is A $35cm$

The given three ropes are $7$m, $12$ m $95$cm and $3$m$85$cm long. We know that $1$m=$100$cm, therefore,

The length of the respective ropes will be:

1st rope $=7\times 100=700$cm

2nd rope $=(12\times 100)+95=1200+95=1295$cm

3rd rope $=(3\times 100)+85=300+85=385$cm

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

$700=2\times 2\times 5\times 5\times 71295=5\times 7\times 37385=5\times 7\times 11$

The highest common factor (HCF) is $5\times 7=35$

Hence, the greatest possible length that can be used to measure these ropes is $35$cm.