Practice | Hashtable

31. In every 30 minutes the time of a watch increases by 3 minutes. After showing the correct time at 5 am , what time will the watch show after 6 hours ?

A. 10 : 54 am

B. 11 : 30 am

C. 11 : 36 am

D. 11 : 42 am

Discuss

Solution:

Time gained in 1 hour = 6 minutes
Time gained in 6 hours = (6 × 6) minutes = 36 minutes
After 6 hours, the correct time is 11 : 00 am and the watch will show 11 : 36 am.

32. A watch is 1 minute slow at 1 pm on Tuesday and 2 minutes fast at 1 pm on Thursday. When did it show the correct time = ?

A. 1 : 00 am on Wednesday

B. 5 : 00 am on Wednesday

C. 1 : 00 pm on Wednesday

D. 5 : 00 pm on Wednesday

Discuss

Solution:

Time from 1 pm on Wednesday to 1 pm on Thursday = 48 hours
So, the watch gains (1 + 2) minute or 3 minutes in 48 hours.
Now, 3 minutes are gained in 48 hours
So, 1 minute is gained in

(\frac{48}{3})

= 16 hours.
Thus, the watch showed the correct time 16 hours after 1 pm on Tuesday, i.e., 5 am on Wednesday

33. Henry started a trip into the country between 8 am and 9 am when the hand of clock were together, He arrived at his destination between 2 pm and 3 pm when the hands of the clock were exactly 180° apart. How long did he travel ?

A. 6 hours

B. 7 hours

C. 9 hours

D. 11 hours

Discuss

Solution:

To be together between 8 am and 9 am, the minute hand has to gain 40 minutes spaces.
55 minutes spaces are gained in 60 minutes.
40 minutes space are gained in

(\frac{60}{55} \times 40)

minutes =

43 \frac{7}{11}

minutes
So, Henry started his trip at

43 \frac{7}{11}

minutes past 8 am.
Now, to be 180° apart, the hands must be 30 minutes spaces apart.
At 2 pm, they are 10 minutes spaces apart.
∴ The minute hand will have to gain (10 + 30) = 40 minutes spaces.
As calculate above, 40 minutes spaces are gained in

43 \frac{7}{11}

minutes.
So, Henry's trip ended at

43 \frac{7}{11}

minutes past 2 pm
∴ Duration of travel = Duration from

43 \frac{7}{11}

minutes past 8 am to

43 \frac{7}{11}

minutes past 2 pm = 6 hours

34. Between 5 and 6, a lady looked at her watch and mistaking the hour hand for the minute hand, she thought that the time was 57 minutes earlier than the correct time. The correct time was = ?

A. 12 minutes past 5

B. 24 minutes past 5

C. 36 minutes past 5

D. 48 minutes past 5

Discuss

Solution:

Since the time read by the lady was 57 minutes earlier than the correct time, so the minute hand is (60 - 57) = 3 minutes spaces behind the hour hand.
Now, at 5 o'clock, the minute hand is 25 minutes spaces behind the hour hand.
To be 3 minutes spaces behind, it must gain (25 - 3) = 22 minutes spaces.
55 minutes spaces are gained in 60 minutes.
22 minutes spaces are gained in

(\frac{60}{55} \times 22)

= 24 minutes
Hence, the correct time was 24 minutes past 5.

35. How many times are the hour hand and the minute hand of a clock of a right angles during their motion from 1 : 00 pm to 10 : 00 pm ?

A. 9

B. 10

C. 18

D. 20

Discuss

Solution:

The duration from 1 : 00 pm to 10 : 00 pm is 9 hours and during each of these 9 hours the hands of the clock are at right angles twice.
So, required number = 9 × 2 = 18

36. Wall clock gains 2 minutes in 12 hours, while a table clock loses 2 minutes every 36 hours. Both are set right at 12 noon on Tuesday. The correct time when both show the same time next would be = ?

A. 12:30 at nights, after 130 days

B. 12 noon, after 135 days

C. 1:30 at nights, after 130 days

D. 12 midnight, after 135 days

Discuss

Solution:

After 12 days, i.e., after 12 × 24 hours clock A will gain 48 minutes and will show 12 : 48 noon.
After 12 days, i.e., after 12 × 24 hours clock B will loose 16 minutes and will show 11 : 44 am
The two clocks will show the same time after time after 135 days.
The time difference has to be 12 hours between then = 720 minutes.
A will gain 540 minutes in 135 days.
B will loose 180 minutes in 135 days, total 720 minutes.
Further if we consider only time then the problem becomes simpler
Total difference of minutes between the times shown by the clocks after 36 hours
⇒

\frac{16}{3}

minutes difference in 1 day
⇒ 12 × 60 minutes difference in

\frac{3}{16}

× 12 × 60 = 135 days
∴ 12 noon, after 135 days

37. A clock is displaying correct time at 9 am on Monday. If the clock loses 12 minutes in 24 hours, then the actual time when the clock indicates 8 : 30 pm on Wednesday of the same week is = ?

A. 8 pm

B. 7 pm

C. 9 pm

D. 8 : 59 : 45 pm

Discuss

Solution:

Time interval from 9 am on Monday to 8 : 30 pm on Wednesday.

\begin{aligned} = (24 \times 2.5) - 0:30 hours \\ = 60 - 0 :30 hours \\ =  59 hours 30 minutes \\ = 59 \frac{30}{60} \\ = 59 \frac{1}{2} \\ = \frac{119}{2} hours \\ Also 24 hours - 12 minutes \\ = 23 hours 48 minutes \\ = 23 + \frac{48}{60} \\ = 23 \frac{4}{5} \\ = \frac{119}{5} hours \\ ∴ \frac{119}{2} hours of this clock \\ = \frac{24 \times 5}{119} \times \frac{119}{2} \\ = 60 hours \\ (60 - \frac{119}{2}) hours \\ = \frac{120 - 119}{2} hours \\ = \frac{1}{2} hours \\ = 30 minutes \end{aligned}

Hence, the correct time is 30 minutes after 8:30 pm i.e., 9 pm

38. A wall-clock takes 9 seconds in tinging at 9 o'clock. The time, it will take in tinging at 11 o'clock, is = ?

A. 10 seconds

B. 1.80 seconds

C. 11 seconds

D. 11.25 seconds

Discuss

Solution:

There are 8 intervals in 9 tinging 10 intervals in 11 tinging.
Time duration of 8 intervals = 9 seconds
∴ Required time = Duration of 10 intervals

\begin{aligned} = (\frac{9}{8} \times 10) seconds \\ = 11.25 seconds \end{aligned}

39. A mechanical grandfather clock is at present showing 7 hours 40 minutes 6 seconds. Assuming that it loses 4 seconds in every hour, what time will it show after exactly $6 \frac{1}{2}$ hours ?

A. 14 hours 9 minutes 34 seconds

B. 14 hours 9 minutes 40 seconds

C. 14 hours 10 minutes 6 seconds

D. 14 hours 10 minutes 32 seconds

Discuss

Solution:

\begin{aligned} Time lost in 6 \frac{1}{2} hours \\ = (6 \frac{1}{2} \times 4) \sec \\ = 26 \sec \end{aligned}

Correct time after

6 \frac{1}{2}

hours
= 7 hours 40 minutes 6 seconds + 6 hours 30 minutes
= 14 hours 10 minutes 6 seconds
Time show by the clock
= 14 hours 10 minutes 6 seconds - 26 sec
= 14 hours 9 minutes 40 seconds

40. A clock strikes once at 1 o'clock, twice at 2 o'clock, thrice at 3 o'clock and so on. What is the total number of strikings in a day = ?

A. 136

B. 146

C. 156

D. 166

Discuss

Solution:

Total number of strikings

\begin{aligned} = 2 (1 + 2 + 3 + . . . . . + 12) \\ = 2 \times \frac{12 \times 13}{2} \\ = 156 \end{aligned}