| 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 |
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 |
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 |
| ? 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.
