Three pieces of timber, 42m, 49m, and 63m long, have to be divided into planks of the same length. What is the greatest possible length of each plank (in m)?

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answer is D.

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Detailed Solution

The given data is as follows.
There are three pieces of timber of lengths 42m, 49m and 63m respectively. They have to be divided into planks of the same length.
We are required to find the greatest possible length of each plank.
We take the HCF of the above numbers in cm using the division method.
The lengths are 42m, 49m and 63m.
We locate the biggest number among the given numbers and divide it by the smallest available number. Afterward, we use the remainder thus obtained to divide the smallest number. This division continues till no further division is possible.

4216342 21 ¯ 4242 ¯ ​ 2 0

We will now check the divisibility of the other number by 21 in the following way.

2124942 7 ¯ 2121 ¯ 3 0

Thus, the required HCF of the numbers by division method is 7.
Therefore, the required greatest possible length of each plank is 7m.
Hence the correct answer is option (4).

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