# Clock - Aptitude Questions and Answers Part 2

6. Find the time between 2pm and 3pm when the two hands of the clock will point towards the opposite sides but will be in a straight line.

 a. 25 1 minutes before 3 pm 11
 b. 38 7 minutes before 3 pm 11
 c. 43 7 minutes past 2 pm 11
 d. 50 5 minutes past 2 pm 11

 Answer: c. 43 7 minutes past 2 pm 11

Explanation:

Tip:
In one hour, MINUTE hand travels 60 minutes
HOUR hand travels just 5 minute spaces
Thus,
MINUTE hand gains (60 - 5) = 55 minutes over HOUR hand in 60

At 2pm hour hand and minute hand difference = 10 minutes

So to be in straight line and opposite direction between 2 and 3, minute hand must be 30 minutes ahead of the hour hand

For 30 minutes ahead, minute hand must travel (30 + 10) = 40 minutes more
In 60 minutes, minute hand gains 55 min.
In ? minutes it gains 40 minutes
 ∴ ? = 40 x 60 = 43 7 minutes past 2 pm 55 11

7. Ram's teacher asked him to set the two hands of the clock between 10 am and 11 am such that they are 8 minutes apart. What time will the clock indicate for such settings?

 a. 43 9 minutes past 10 o' clock and 3 3 minutes past 11 o' clock 11 11
 b. 43 9 minutes past 10 o' clock and 58 9 minutes before 11 o' clock 11 11
 c. 43 9 minutes past 10 o' clock and 3 3 minutes before 11 o' clock 11 11
 d. 3 3 minutes before 11 o' clock and 63 3 minutes past 10 o' clock 11 11

 Answer: c. 43 9 minutes past 10 o' clock and 3 3 minutes before 11 o' clock 11 11

Explanation:

Tip:
In one hour, MINUTE hand travels 60 minutes
HOUR hand travels just 5 minute spaces
Thus,
MINUTE hand gains (60 - 5) = 55 minutes over HOUR hand in 60 minutes

At 10 o'clock hour hand & minute hand difference = 50 minutes.
So to be 8 min apart, minute hand must be at (50 - 8 =) 42 minutes or (50 + 8 =) 58 minute s position
For 42 minutes, minute hand must travel 42 minutes more
In 60 minutes, minute hand gains 55 min.
In ? minutes it gains 42 minutes
 ∴ ? = 42 x 60 = 43 9 minutes past 10 o' clock 55 11
For 58 minutes, minute hand must travel 58 minutes more
In 60 minutes, minute hand gains 55 min.
In ? minutes it gains 58 minutes
 ∴ ? = 58 x 60 = 63 3 minutes past 10 o' clock = 1 hour + 3 3 minutes 55 11 11
 That means 3 3 minutes past 11 o' clock 11

8. How much does a clock gain or lose in 24 hrs if the minute hand and hour hand meet in every 62 minutes?

 a. 56 65 minutes Loss 11
 b. 66 5 minutes Loss 11
 c. 72 7 minutes Gain 11
 d. 78 74 minutes Gain 11

 Answer: d. 78 74 minutes Gain 11

Explanation:

Tip:
In one hour, MINUTE hand travels 60 minutes
HOUR hand travels just 5 minute spaces
Thus,
MINUTE hand gains (60 - 5) = 55 minutes over HOUR hand in 60 minutes

If the minute hand wants to meet the hour hand, it can meet only after it travels 60 minutes.
So,
In 60 minutes, minute hand gains 55 min.
In ? minutes it gains 60 minutes
 ∴ ? = 60 x 60 = 65 5 minutes = Minute and hour hand meet after these many minutes 55 11
But as per the given condition,
Hands meet after 62 minutes i.e. earlier
 So the clock gains (65 5 - 62) = 38 minutes 11 11
 So in 62 minutes clock gains 38 minutes 11
In 24 hours clock gains ? minutes
 ? minutes = 38 x (24 x 60 minutes) = 6080 = 78 74 minutes 11 63 minutes 77 11

9. Find the time in the clock after 9pm when the two hands of the clock will form a 90 degree angle between themselves.

a. At 3 pm
b. At 9 pm
 c. At 29 8 minutes before 10 pm 11
 d. At 32 8 minutes past 9 pm 11

 Answer: d. At 32 8 minutes past 9 pm 11

Explanation:

Tip:
In one hour, MINUTE hand travels 60 minutes
HOUR hand travels just 5 minute spaces
Thus,
MINUTE hand gains (60 - 5) = 55 minutes over HOUR hand in 60

At 9 pm hour hand and minute hand difference = 45 minutes
They already are at right angle. We want after 9 pm.
For right angle, minute hand must be 15 minutes behind
For 15 minutes behind, minute hand must travel (45 - 15) = 30 minutes more
In 60 minutes, minute hand gains 55 min.
In ? minutes it gains 30 minutes
 ∴ ? = 30 x 60 = 32 8 minutes past 9 pm 55 11

10. To ensure that he is not late for exam, Ram's teacher asked him to set the alarm for Monday 11 am. He sets it correctly at 1 am on Sunday but wasn't aware about the fault in the clock. The clock gained 20 minutes for every 24 hours. What would be the actual time when the alarm would go off?

a. 28 minutes 20 seconds before 10 am
b. 31 minutes 40 seconds past 10 am
c. 28 minutes 20 seconds past 11 am
d. 31 minutes 40 seconds past 11 am

Answer: b. 31 minutes 40 seconds past 10 am

Explanation:

From 1.00 am Sunday to 11 am Monday we have
24 hours (till 1 am Mon) + 10 hours = 34 hours
20 minutes gained in 24 hours
∴ ? minutes  gained in 34 hours
∴ ? = 28.333 minutes = 28 minutes 20 seconds
Alarm will go off at 11 am
But actual time will be less than that because clock had gained time.
∴ Actual time = 11am - 28 minutes 20 seconds = 31 minutes 40 seconds past 10 am.