Question

a clock is shows 8:42 p.m. after how many minutes both the hands of the clock will make an angle of 150 degree

Answer 1

Answer:

1:42 a.m.

Step-by-step explanation:

a clock is complete circle which means 360 degree angle

So in one hour it covers 30 degree

which means 150 degree will be cover in 5 hours .

So just add 5 hours to 8:42p.m.

Answer 2

Answer:

Solving conceptually :-

Minute hand create 360° in one hour with respect to number 12.

So minute hand create 6° in one minute. 1

Hour hand create 360° in 12 hour i.e. 30° in one hour.

So hour hand create 1/2° in 1 minute. 2

Current position  :-

At 5:30

Minute hand is at 30 min -  30*6=180°

Hour hand is at 5h30m -  30*5+30*0.5=165°

Current difference :- 180-165=15°

Difference increment per minute = 6 - 1/2 = 5.5  from 1 and 2.

=Current difference + (per minute difference ) (minutes after which hands will be at right angle ) = right angle

Now 15+5.5x =90

x =( 90-15)/ 5.5 = 13+

 

Finally right angle will be at 5:43 plus some seconds