SNAP Clocks Questions

The hour hand and the minute hands will be opposite to each other when the angle between them= $$180^{\circ\ }$$.

At 9PM, angle between the two hands= 270$$^{\circ\ }$$

The minute hand covers 360$$^{\circ\ }$$ in 60 minutes. So, in 1 minute, it covers $$\ \frac{\ 360^{\circ\ }}{60}$$= 6$$^{\circ\ }$$

Similarly for the hour hand, it covers 360$$^{\circ\ }$$ in 12 hours or 720 minutes. 

.'. The hour hand covers $$\ \frac{\ 360^{\circ\ }}{720}$$= 0.5$$^{\circ\ }$$.

Using the concept of relative speed, since both the hands move in the same directions, the effective speed= (6-0.5)$$^{\circ\ }$$ =5.5 or $$\ \frac{\ 11}{2}$$ degrees per minute.

Effective distance to cover= $$270^{\circ}-180^{\circ\ }=\ 90^{\circ\ }$$

Therefore time taken= $$\ \frac{\ 90}{\ \frac{\ 11}{2}}=\ \ \frac{\ 180}{11}=\ 16\ \frac{\ 4}{11}$$ minutes after 9 PM. 

Option B is our answer.

A watch is a minute slow at 1 p.m. on Tuesday and 2 minutes fast at 1 p.m. on Thursday.

So the watch gains 3 minutes in 48 hours.

It will show the exact time when it would have gained 1 minute from the initial state.

1/3=x/48

x=16 hours.

i.e at 5:00 am Wednesday

Option B

The clock strikes thrice at 3.

There are two intervals between 3 strikes. For nine strikes there will be 8 intervals.

2 intervals take 6 seconds. => 8 intervals will take 24 seconds.

Let $$x$$ minutes be the required time.

then 12 noon - 10:27 am = $$x$$

         $$x$$ = 1 hour 33 minutes = 93 minutes