A person goes to a market between 4 p.m. and 5 p.m. When he comes back, he finds that the hour hand and minute hand have interchanged their positions. For how much time (approximately) was he out of his house?

55.25 minutes

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55.30 minutes

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55.34 minutes

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55.38 minutes

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None of these

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Solution

The correct option is D 55.38 minutes
Let us assume that he was out of the house for 't' min.
So angle formed by min hand $= 6 \times t$
Angle formed by hour hand = $0.5 \times t$
Now, 0.5 $\times$ t + 6 $\times$ t = 360
$\Rightarrow 6.5 t = 360$
$\Rightarrow 6.5 t = 360 t = \frac{360}{6.5} = 55.38 m i n$

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A person goes to a market between 4 p.m. and 5 p.m. When he comes back, he finds that the hour hand and minute hand have interchanged their positions. For how much time (approximately) was he out of his house?

The correct option is D 55.38 minutesLet us assume that he was out of the house for 't' min. So angle formed by min hand =6×t Angle formed by hour hand = 0.5×t Now, 0.5 × t + 6 × t = 360 ⇒6.5 t=360 ⇒6.5 t=360t=3606.5=55.38 min