# What time does the clock show when the hour hand is between 3 and 4 and the angle between the two hands of the clock is 50°?   Option 1)     min past 3   Option 2)   min past 3   Option 3)   min past 3   Option 4)   None of these   Option 5)   Both (1) and (2)

We know that In 60 Minutes,

Minute hand covers 360 degrees.

Hour hand covers 30 degrees.

In every 60 Min Minute hand covers 330 degrees more than the hour hand.

330 degree in minutes = 55 Minutes

So, we can conclude that in every 60 Minute Minute hand is 55 Minute ahead.

To be 1 minute ahead, time taken by minute hand = 60/55 = 12/11

Case 1 - When the minute hand is behind

The distance while there will be time 3 'o' clock = 15 minutes or 90 degree

distance to be cover to make 50 degrees = 90 - 50 => 40 degree or 25/3 min

time taken after 3 = 25/3 x 12/11 => 9 (1/11)

So the exact time when the hands will be together = 3: 09 (1/11)

Case-2 When the minute hand is ahead

The distance while there will be time 3 'o' clock = 15 minutes or 90 degree

distance to be cover to make 50 degrees = 90 + 50 => 140 degree or 70/3 min

time taken after 3 = 70/3 x 12/11 => 25 (5/11)

So, the exact time when the hands will be together = 3: 25 (5/11)

Thus, Option(4) will be the answer.

Boost your Preparation for JEE Main 2021 with Personlized Coaching

Exams
Articles
Questions