# CRE 2 - Faulty Clock | LR - Clocks

**CRE 2 - Faulty Clock | LR - Clocks**

A faulty clock is set right at 1 p.m.. If it gains one minute an hour, what time will it show at 6 p.m. the same day.

- (a)
6 p.m.

- (b)
6:05 p.m.

- (c)
5:55 p.m.

- (d)
None of these

Answer: Option B

**Explanation** :

Time gained in 1 hour = 1 min

Actual time interval from 1 p.m. till 6 p.m. is 5 hours.

∴ In 5 hours, the faulty clock would have gained 5 minutes.

∴ The faulty clock will show 5 minutes more than actual time.

⇒ Time shown by faulty clock will be 6:05.

Hence, option (b)

Workspace:

**CRE 2 - Faulty Clock | LR - Clocks**

A watch gains time uniformly was observed to be 2 min slow at 6:00 a.m. on a day. On the same day at 8:00 p.m. the watch was 2 min. fast. When did the watch show the correct time?

- (a)
3 p.m.

- (b)
12 noon

- (c)
1 p.m.

- (d)
12:30 p.m.

Answer: Option C

**Explanation** :

From 2 minutes behind at 6 am the faulty clock goes 2 minutes ahead at 8 pm.

∴ The faulty clock covers 4 minutes extra during these 14 hours.

⇒ The faulty clock gains 4 minutes in 14 hours or 2 minutes in 7 hours.

Now, after 6 a.m. for the faulty to clock to show correct time, it needs to gain 2 minutes to be able to show the same time as actual clock.

To gain 2 minutes faulty clock will take 7 hours.

∴ At 6 a.m. + 7 hours = 1 p.m. the faulty clock will show correct time.

Hence, option (c).

Workspace:

**CRE 2 - Faulty Clock | LR - Clocks**

A watch which gains uniformly, is 2 minutes slow, at noon on Tuesday and is 4 minutes 48 seconds fast at 2 p.m. on the following Tuesday. When was it correct?

- (a)
2 p.m. on Wednesday

- (b)
2 p.m. on Friday

- (c)
2 p.m. on Tuesday

- (d)
2 p.m. on Thursday

Answer: Option D

**Explanation** :

Actual time interval from Tuesday noon to the following Tuesday at 2 p.m. = 7 days 2 hours = 170 hours

The watch gains $\left(2+4\frac{48}{60}\right)$ i.e. $6\frac{4}{5}$ min in 170 hours.

To show correct time, the watch needs to gain 2 minutes from the start.

∴ The watch gains 2 minutes in = $\left(\frac{170}{6\frac{4}{5}}\times 2\right)$ i.e. 50 hours

Now, 50 hours = 2 days 2 hours

∴ 2 days from Tuesday noon = 2 p.m. on Thursday

Hence, option (d).

Workspace:

**CRE 2 - Faulty Clock | LR - Clocks**

A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 O'clock, the true time is :

- (a)
$5\frac{3}{11}$ minutes past 3

- (b)
4 p.m.

- (c)
$5\frac{2}{11}$ minutes past 4

- (d)
$2\frac{5}{11}$ minutes past 5

Answer: Option B

**Explanation** :

The faulty clock gains 5 seconds every 3 minutes.

⇒ Faculty clock covers 185 seconds for every 180 seconds covered by actual clock

⇒ $\frac{\mathrm{Time}\mathrm{covered}\mathrm{by}\mathrm{faulty}\mathrm{clock}}{\mathrm{Actual}\mathrm{time}\mathrm{covered}}$ = $\frac{185}{180}$ = $\frac{37}{36}$

From 7 a.m. till quarter past 4 p.m., the faulty clock covers 9$\frac{1}{4}$ = $\frac{37}{4}$ hours

⇒ $\frac{\mathrm{Time}\mathrm{covered}\mathrm{by}\mathrm{faulty}\mathrm{clock}}{\mathrm{Actual}\mathrm{time}\mathrm{covered}}$ = $\frac{37}{36}$

⇒ $\frac{{\displaystyle \raisebox{1ex}{$37$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}}{\mathrm{Actual}\mathrm{time}\mathrm{covered}}$ = $\frac{37}{36}$

⇒ Actual time covered = 9 hours.

∴ Actual time is 9 hours after 7 am. i.e., 4 p.m.

Hence, option (b)

Workspace:

**CRE 2 - Faulty Clock | LR - Clocks**

A clock is set right at 1 p.m. if it gains one minute an hour, what is the true time when the clock indicates 6 p.m. the same day.

- (a)
$55\frac{5}{61}$ min past 4 p.m.

- (b)
$55\frac{5}{61}$ min past 5 p.m.

- (c)
$53\frac{5}{61}$ min past 4 p.m.

- (d)
None of these

Answer: Option B

**Explanation** :

The faulty clock gains 1 minute every 60 minutes.

⇒ Faculty clock covers 61 minutes for every 60 minutes covered by actual clock

⇒ $\frac{\mathrm{Time}\mathrm{covered}\mathrm{by}\mathrm{faulty}\mathrm{clock}}{\mathrm{Actual}\mathrm{time}\mathrm{covered}}$ = $\frac{61}{60}$

From 1 p.m. till 6 p.m., the faulty clock covers 5 hours

⇒ $\frac{\mathrm{Time}\mathrm{covered}\mathrm{by}\mathrm{faulty}\mathrm{clock}}{\mathrm{Actual}\mathrm{time}\mathrm{covered}}$ = $\frac{61}{60}$

⇒ $\frac{{\displaystyle 5}}{\mathrm{Actual}\mathrm{time}\mathrm{covered}}$ = $\frac{61}{60}$

⇒ Actual time covered = $\frac{300}{61}$ = 4 hours 55$\frac{5}{61}$ minutes.

∴ Actual time is 4 hours 55$\frac{5}{61}$ minutes after 1 p.m. i.e., 5 : 55$\frac{5}{61}$ p.m.

Hence, option (b)

Workspace:

**CRE 2 - Faulty Clock | LR - Clocks**

A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on the 4^{th} day?

- (a)
10 p.m.

- (b)
11 p.m.

- (c)
9 p.m.

- (d)
8 p.m.

Answer: Option B

**Explanation** :

The faulty clock loses 16 minutes every 24 hours.

∴ The faulty clock loses 2 minutes every 3 hours.

⇒ Faculty clock covers 178 minutes for every 180 minutes covered by actual clock

⇒ $\frac{\mathrm{Time}\mathrm{covered}\mathrm{by}\mathrm{faulty}\mathrm{clock}}{\mathrm{Actual}\mathrm{time}\mathrm{covered}}$ = $\frac{178}{180}$ = $\frac{89}{90}$

From 5 a.m. till 10 p.m. on 4^{th} day, the faulty clock covers 89 hours.

⇒ $\frac{\mathrm{Time}\mathrm{covered}\mathrm{by}\mathrm{faulty}\mathrm{clock}}{\mathrm{Actual}\mathrm{time}\mathrm{covered}}$ = $\frac{89}{90}$

⇒ $\frac{{\displaystyle 89}}{\mathrm{Actual}\mathrm{time}\mathrm{covered}}$ = $\frac{89}{90}$

⇒ Actual time covered = 90 hours.

∴ Actual time is 90 hours 5 a.m. i.e., 11 p.m. on 4^{th} day.

Hence, option (b).

Workspace:

**CRE 2 - Faulty Clock | LR - Clocks**

A clock is set right at 7 a.m. on Monday. The clock gains 10 minutes in every 24 hours. What will be the true time when the clock indicates 5 p.m. on the following Wednesday?

- (a)
4:40 p.m.

- (b)
4:30 p.m.

- (c)
4:36 p.m.

- (d)
4:46 p.m.

Answer: Option C

**Explanation** :

The time interval from Monday 7 a.m. to Wednesday 5 p.m. = 58 hours

When a normal clock covers 24 hours, the faulty clock covers 24 hours and 10 minutes = 145/6 hours.

∴ 58 hrs of faulty clock = $\frac{24}{145/6}$ × 58 hours = 57 hours 36 minutes.

∴ Required correct time is 57 hours and 36 minutes after 7 a.m. on Monday i.e., 4 : 36 p.m. on Wednesday.

Hence, option (c)

Workspace:

**CRE 2 - Faulty Clock | LR - Clocks**

How much does a watch gain or lose per day, if its hands coincide every 64 minutes?

- (a)
loses 96 minutes

- (b)
loses 90 minutes

- (c)
gains $36\frac{5}{11}$ minutes

- (d)
gains $32\frac{8}{11}$ minutes

Answer: Option D

**Explanation** :

Let us calculate time interval for hands of a normal clock to coincide.

The two hands coincide at 12 O'clock. Next they will coincide between 1 and 2 O'clock.

⇒ $\left|30\mathrm{h}-\frac{11}{2}\mathrm{m}\right|$ = 0

⇒ $\left|30\times 1-\frac{11}{2}\mathrm{m}\right|$ = 0

⇒ 30 - $\frac{11}{2}$m = 0

⇒ m = $\frac{60}{11}$ = 5$\frac{5}{11}$ minutes.

∴ The two hands coincide again at 1 : 5$\frac{5}{11}$.

⇒ From 12 O'clok till 1 : 5$\frac{5}{11}$ it takes 65$\frac{5}{11}$ minutes for the two hands to coincide again.

For a normal clock, hands coincide every $65\frac{5}{11}$ minutes, but for the faulty clock hands coincide every 64 minutes.

[If you look at the faulty clock you would get a sense that $65\frac{5}{11}$ minutes have passed when actually only 64 minutes have passed.]

∴ The faulty clock gains $1\frac{5}{11}$ minutes every 64 minutes.

∴ Time gained in a day i.e., 24 hours = $\frac{1\frac{5}{11}}{64}\times 24\times 60$ = $\frac{360}{11}$ = $32\frac{8}{11}$ minutes.

Hence, option (d).

Workspace:

**CRE 2 - Faulty Clock | LR - Clocks**

One evening, Aakash goes out for a drive, sometime between 4 O'clock and 5 O’clock. When he gets back, sometime between 7 O’clock and 8 O’clock, he noticed that the minute and hour hands have interchanged their positions exactly with what they were when he started out. Approximately how long was his drive?

- (a)
2 hours 15 mins

- (b)
1 hour 12 mins

- (c)
2 hours

- (d)
2 hours 46 mins

Answer: Option D

**Explanation** :

Since the hands swap positions when he returns

When Aakash goes out hour hand is in between 4 and 5, while minute hand is in between 7 and 8.

When Aakash comes in hour hand is in between 7 and 8, while minute hand is in between 4 and 5.

⇒ Aakash left when the time was 4 : (35 - 40), and

He came back when the time was 7 : (20 - 25).

∴ The minimum time Aakash was out would be 2 hours 40 minutes (4:40 till 7:20), and

The maximum time Aakash was out would be 2 hours 50 minutes (4:35 till 7:25)

The possible option for his duration out of home is option (d).

Hence, option (d).

Workspace:

**CRE 2 - Faulty Clock | LR - Clocks**

There are two clocks on a wall, both set to show the correct time at 6 a.m. The faster clock gains 1 minute every hour while the slower clock looses 2 minutes every hour. If the faster clock shows the time as 12 minutes past 6 p.m. on the same day, then what time does the other watch show?

- (a)
5:48 p.m.

- (b)
6 p.m.

- (c)
6:05 p.m.

- (d)
5:36 p.m.

- (e)
None of these

Answer: Option D

**Explanation** :

From 6 am till 6 pm, the faster clock will gain 12 minutes, hence it shows the time as 6:12 pm.

⇒ The actual time is 6 pm.

Now, the slower clock will lose 24 minutes from 6 am till 6 pm. Hence the time it will show will be 24 minutes less than the actual time.

∴ The slower clocks will show the time as 5:36 pm.

Hence, option (d).

Workspace:

**CRE 2 - Faulty Clock | LR - Clocks**

A watch, which gains uniformly, was observed to be 15 minutes slow at 12 noon on 10^{th} March. It was noticed 25 minutes fast at 8 p.m., 18^{th} March. When did the watch show the correct time?

- (a)
3 pm on 13

^{th}March - (b)
11 pm on 12

^{th}March - (c)
1 am on 13

^{th}March - (d)
1 pm on 14

^{th}March - (e)
None of these

Answer: Option A

**Explanation** :

From 12 noon on 10^{th} March till 8 pm on 18^{th} March, total time elapsed is 200 hours.

The clock was 15 mins slow initially and finally was 25 mins ahead, hence it gained 40 mins.

Clock gained 40 mins in 200 hours.

For the clock to show correct time, it needs to gain 15 mins from the start.

Time taken to gain 15 mins = 15/40 × 200 = 75 hours.

75 hours from 12 noon 10^{th} March will be 3 pm on 13^{th} March.

Hence, option (a).

Workspace:

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