?
The reflex angle between the hands of a clock at 10.25 is:
Answer & Solution
Correct Answer:
Option
D
Angle traced by hour hand in $$\frac{{125}}{{12}}$$ hrs
$$\eqalign{ & = {\left( {\frac{{360}}{{12}} \times \frac{{125}}{{12}}} \right)^ \circ } \cr & = 312{\frac{1}{2}^ \circ } \cr} $$
Angle traced by minute hand in 25 min
$$\eqalign{ & = {\left( {\frac{{360}}{{60}} \times 25} \right)^ \circ } \cr & = {150^ \circ } \cr} $$
$$\eqalign{ & \therefore {\text{Reflex angle}} \cr & = {360^ \circ } - {\left( {312\frac{1}{2} - 150} \right)^ \circ } \cr & = {360^ \circ } - 162{\frac{1}{2}^ \circ } \cr & = 197{\frac{1}{2}^ \circ } \cr} $$
$$\eqalign{ & = {\left( {\frac{{360}}{{12}} \times \frac{{125}}{{12}}} \right)^ \circ } \cr & = 312{\frac{1}{2}^ \circ } \cr} $$
Angle traced by minute hand in 25 min
$$\eqalign{ & = {\left( {\frac{{360}}{{60}} \times 25} \right)^ \circ } \cr & = {150^ \circ } \cr} $$
$$\eqalign{ & \therefore {\text{Reflex angle}} \cr & = {360^ \circ } - {\left( {312\frac{1}{2} - 150} \right)^ \circ } \cr & = {360^ \circ } - 162{\frac{1}{2}^ \circ } \cr & = 197{\frac{1}{2}^ \circ } \cr} $$
Join the Discussion
Login to post a comment or share your explanation.
Login1 hour = 30 degree (360/12)
If the minute hand move one minute the hour hand move 0.5 degree (30/60) "30 degree,60 minute"
Overall total
For minute 25 x 6=150 degree
+
For hour 0.5x 25 = 12.5
Balance 30 - 12.5 =17.5degree
Add balance hour 11 to 12 =30 degree
Total= 150 +17.5 + 30 =197.5 degree
1 hour = 30 degree (360/12)
If the minute hand move one minute the hour hand move 0.5 degree (30/60) "30 degree,60 minute"
Overall total
For minute 25 x 6=150 degree
+
For hour 0.5x 25 = 12.5
Balance 30 - 12.5 =17.5degree
Add balance hour 11 to 12 =30 degree
Total= 150 +17.5 + 30 =197.5 degree
This is true answer
Angel between them is 162.5 but
Reflex angle is 360-162.5=197.5
Therefore this is correct answer.
a - angle
a = 30×hr-11/2×min
Hr = 10
Min = 25
a = 30×10-11/2×25
= 300-275/2
= 162.5
Reflex angle = 360-162.5 =197.5
= 30×10 - 11×25/2
300-275/2
300-137.5
= 162.5
Reflex angle =360 - 162.5 = 197.5
true answer=162.5