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In a morning walk three persons step off together, their steps measure 80 cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that he can cover the distance in complete steps?

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122 m 40 cm

110 m 20 cm

120 m 35 cm

105 m 55 cm

answer is D.

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Detailed Solution

Given,
Length of the step of first-person

= 80 cm

Length of the step of second person

= 85 cm

Length of the step of third-person

= 90 cm

The prime factorisation of 80, 85 and 90 is as follows.

2 80, 85, 90 2 40, 85, 45 2 20, 85, 45 2 10, 85, 45 3 5, 85, 45 3 5, 85, 15 5 5, 85, 5 17 1, 17, 1 1,1,1

LCM = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 17

\Rightarrow LCM = 12240

Minimum Distance = LCM (80, 85, 90)

\Rightarrow 12240 cm

\Rightarrow 122 m 40 cm

(As 100 cm = 1 m)
Therefore, the minimum distance each should walk so that he can cover the distance in complete steps is 122 m 40 cm.
Hence, option 4 is correct.

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