## Clock Problems for infosys placement

Below are three problems based on clocks, which you can expect in infosys and other companies placement test.

**Question 1**

Three analog clocks were set to correct time. First one run with the exact time. Second one loss one hour per day. Third one gains one hour per day. After how many days will they show the same time?

a)180 days & 10 hours b)287 days & 12 hours c)212 days d)199 days

**Answer :**b) 287 days & 12 hours

Solution :

Let a day be a cycle of 24 hours.

First one completes a cycle within a day

Second one completes a cycle in 25 hours

And third one completes a cycle in 23 hours.

Now, the LCM of 23,24,25 is 23 x 24 x 25 = 13800.

First one completes a cycle within a day

Second one completes a cycle in 25 hours

And third one completes a cycle in 23 hours.

Now, the LCM of 23,24,25 is 23 x 24 x 25 = 13800.

Therefore, after 13,800 hours (least period) they will show the correct time together. (for 24 hours cycle)

i.e., 13,800/24 = 575

On 575th day they will show the correct time.

Since the clocks are analog (12 hours cycle), after 287 days and 12 hours (575/2 = 287.5)they will show the same time.

i.e., 13,800/24 = 575

On 575th day they will show the correct time.

Since the clocks are analog (12 hours cycle), after 287 days and 12 hours (575/2 = 287.5)they will show the same time.

**Question 2**

Three clocks were set to true time and starts to run together, makes a beep sound at intervals of 8,10 and 12 minutes respectively. In 2 days, how many times do they will make the sound together?

a)12 b)15 c)25 d)30

**Answer :**c)25

Solution:

The clocks make sound at intervals of 8, 10 and 12 minutes respectively.

The LCM of 8,10 and 12 is 120.

So the clocks will make sound together after every 120 minutes.

i.e., after every 2 hours.

The LCM of 8,10 and 12 is 120.

So the clocks will make sound together after every 120 minutes.

i.e., after every 2 hours.

In 2 days(48 hours), they will make the sound together (48/2) = 24 times.

At the end of 2 day,they will make one more beep together.

Therefore, totally (24+1) 25 times beep sound is made together.

Hence the answer is 25 times.

At the end of 2 day,they will make one more beep together.

Therefore, totally (24+1) 25 times beep sound is made together.

Hence the answer is 25 times.

**Question 3**

Three analog clocks were set to the exact time at 12 am and they run together and gain 3, 6 and 9 minutes per hour respectively. At what time, they will show the same time again?

a)2.42am b)12.02am c)1.58pm d)12.02pm

**Answer :**a)2.42am

Solution :

Let an hour(60 minutes) be a cycle.

The clocks complete a cycle early by 3, 6 and 9 minutes respectively.

i.e., a cycle is completed in 57, 54 and 51 minutes respectively.

LCM of 57,54 and 51 is 17442 minutes.

The clocks show the same time after 17442 minutes

The clocks complete a cycle early by 3, 6 and 9 minutes respectively.

i.e., a cycle is completed in 57, 54 and 51 minutes respectively.

LCM of 57,54 and 51 is 17442 minutes.

The clocks show the same time after 17442 minutes

To convert 17442 minutes, we have to divide by 60 :

17442/60 = 17400/60 + 42/60 = 290 hours + 42/60 hours = 290 hours and 42 minutes

(42/60 hours = 42/60 x 60 minutes = 42 minutes)

(42/60 hours = 42/60 x 60 minutes = 42 minutes)

After 290 hours and 42 minutes from 12 am, an analog clock shows 2.42am. (since 290 = 24 x 12 + 2).

Hence, they show the exact time again at 2.42 am .