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A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:
Answer & Solution
Correct Answer:
Option
C
Angle traced by hour hand in 12 hrs = $${360^ \circ }$$
Angle traced by hour hand in 5 hrs 10 min. i.e.,
$$\eqalign{ & \frac{{31}}{6}{\text{hrs}} = {\left( {\frac{{360}}{{12}} \times \frac{{31}}{6}} \right)^ \circ } \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {155^ \circ } \cr} $$
Angle traced by hour hand in 5 hrs 10 min. i.e.,
$$\eqalign{ & \frac{{31}}{6}{\text{hrs}} = {\left( {\frac{{360}}{{12}} \times \frac{{31}}{6}} \right)^ \circ } \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {155^ \circ } \cr} $$
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Login5hrs 10min = 300min + 10min = 310min
5hr 10min/60min = 310min/60min = 31/60
This is how 31/60 happened
Just because of unit conversions
5hr+10/60
31/6hr*30
=155°
So 360°=12 hr.
30° =1 hr
For 5 hr = 150°
Or
In one hr. Min. Rotets by 60
So. 30° = 60 min.
0.5°= 1 min.
So for 10 min = 5°
So total angle = 150°+5° = 155° Ans.
Always use this formula for clock
Angle= | 11/2* 25 - 30 * 10 |
= | -137.5 |
= 137.5
Reflex angle = 360 - 137.5
= 197.5
1/2(60*5+10)
1/2(300+10)
155 Ans
310/60=31/6 min