Determine the greatest possible length which can be used to measure exactly the lengths 7m, 3m 85cm, 12m and 95cm.

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40 cm

25 cm

35 cm

20 cm

answer is C.

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Detailed Solution

Given are three lengths, 7m, 3m 85cm, and 12m 95cm.
We have to determine the greatest possible length which can measure these lengths exactly. So, the greatest length will be the HCF of the given lengths.
Now, we know that 1 m = 100 cm, so converting the given lengths to cm, we get
7 m = 700 cm
3 m and 85 cm = 300 + 85
= 385 cm
12 m and 95 cm = 1200 + 95
= 1295 cm
Now, to get the HCF of the given lengths, we will express 700cm, 385cm and 1295cm as a product of their prime factors as follows,

700 = 2 × 2 × 5 × 5 × 7 385 = 5 × 7 × 11 1295 = 5 × 7 × 37

We can observe that the common factors among the three are 5 and 7.
HCF =

5 × 7

=35
So, the HCF of 700 cm, 385 cm and 1295 cm is 35 cm.
Therefore, the greatest possible length is obtained as 35 cm.
Hence, the correct option is (3).

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