At what time between 10 to 11 O' clock minute and hour hand will coincide or makes 0° angle?

Concept Used:-

In one hour, minute hand moves 360 degree while hour hand moves 30 degrees. So, the ratio of movement of hour to mintue hand is,

\(\Rightarrow r =\dfrac{30}{360}\\ \Rightarrow r =\dfrac{1}{12}\)

Explanation:-

To coincide, minute hand need to be between 10 to 11. Which means minute hand has to be move atleat 50 minutes to reach at 10.

Suppose the required time is X minutes past 10 O' clock.

In X minutes, movement of hour hand = X / 12

So, location of hour hand = 50 + X / 12    

To coincide both the hands we will get the following expression,

⇒ X = 50 + X / 12

⇒ X - 50 = X / 12

Multiply with number 12 both side of equation,

⇒ 12X - 600 = X 

⇒ 12X - X = 600

⇒ 11X = 600

⇒ X = 600 / 11

⇒ X = 54 \(\frac{6}{11} \)

So, the time between 10 to 11 O' clock minute and hour hand will coincide or makes 0° angle is 10 : 54 \(\frac{6}{11} \).

Hence, the correct option is 3.