The length, breadth and height of a room are 8m 25cm, 6m 75cm and 4m 50 cm, respectively. Determine the longest rod which can measure the three dimensions of the room exactly.

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70 cm

75 cm

72 cm

71 cm

answer is B.

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Detailed Solution

Given,
Length of room = 8m 25cm
Breadth of room = 6m 75cm
Height of room = 4m 50cm
We know that 1m = 100cm
Therefore,

8 m 25 c m = (8 × 100) + 25 cm = 825 cm 6 m 75 cm = (6 × 100) + 75 cm = 675 cm 4 m 50 cm = (4 × 100) + 50 cm = 450 cm

Longest rod which can measure the three dimensions of the room exactly
= HCF (Length, Breadth, Height)
= HCF(825,675,450)
Prime factors of 825, 675 and 450 will be,

825 = 5 × 3 × 5 × 11 675 = 5 × 5 × 3 × 3 × 3 450 = 5 × 5 × 3 × 3 × 2

The Highest Common Factor (HCF) of two numbers is the highest possible number that completely divides both numbers.
So, HCF(825,675,450) is

⇒ 5 × 5 × 3 ⇒ 75

Therefore longest rod that can measure three dimensions of the room exactly is 75cm.
Hence the correct option is 2.

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