Question

I left home for bringing milk between $7am$ and $8am$. The angle between the hour-hand and the minute-hand was ${90}^{\circ }$ I returned home between $7am$ and $8am$. Then also the angle between the minute-hand and hour-hand was ${90}^{\circ }$. At what time (nearest to second) did I leave and return home?

• A. $7h18m35s$ and $7h51m24s$
• B. $7h19m24s$ and $7h52m14s$
• C. $7h20m42s$ and $7h53m11s$
• D. $7h21m49s$ and $7h54m33s$

Answer 1

Answer: (D)

$7h21m49s$ and $7h54m33s$

He left between $7am$ and $8am$. The hour-hand and minute-hand was making angle of ${90}^{\circ }$.

So, the hour-hand was between $7$ and $8$ and minute-hand was between $4$ and $5$.

So, leaving time would be between $7:20-7:25$.

After every $12$ minutes, the hour-hand moves one stick ahead.

As the two hands was making ${90}^{\circ }$, so the leaving time would be $7:21$

Thus, the leaving time was $7h21m49s$.

Similarly, the returning time would be $7h54m33s$.

Hence, option D is correct.