Question

Rajesh went out between $5$ and $6$ and returned between $6$ and $7$. He found that the hands of the clock had exactly changed places. When did Rajesh go out?

• A. $31\frac{4}{13}$ min. past $5$
• B. $33\frac{4}{13}$ min. past $5$
• C. $32\frac{4}{13}$ min. past $5$
• D. $32\frac{6}{13}$ min. past $5$
• E. $32\frac{5}{13}$ min. past $5$

Answer 1

The correct option is C $32\frac{4}{13}$ min. past $5$

Rajesh went out between $5$ and $6$ and returned between $6$ and $7$.

He found that the hands of the clock had exactly changed places.

So, when he went out the hour-hand was between $5$ and $6$ and minute-hand was between $6$ and $7$.

And when he came back, the hour-hand was between $6$ and $7$ and minute-hand was between $5$ and $6$.

So, he went out between $5:30-5:35$ and came back between $6:25-6:30$.

Since the hands are exchanged he would have went around $5:32$ and came back around $6:28$.

There is a gap of $4$ between $32$ and $28$.

Thus, he went out at 5 hour $32+\frac{4}{13}$ min.