CLOCK (ERROR)
TYPE 1: When the Minute Hand overtakes the Hour Hand either fast or slow.
Example : If in a clock the minute hand overtakes the hour hand in 65 minutes of correct time then how much does the clock gain or loss in a day ?
a. 24/23 fast
b. 24/123 slow
c. 24/ 23 slow
d. 24/ 123 fast
Sol : 5
After every 65 ━━ minutes , Minute Hand overtakes the Hour Hand.
11
According to question, the Minute Hand overtakes hour Hand in 65 minutes. The Clock is faster than the usual.
We know that ,
5
65 ━ ─ Given Time
11
━━━━━━━━━━━ x Total Time
Given Time
5
65 ━ ─ 65
11
= ━━━━━━━━━━━ x 24 hours
65
5
= ━━━━━ x 24 hours
11 x 65
24
= ━━━ hrs fast.
143
Example : If in a clock the minute hand overtakes the Hour hand in 60 minutes of correct time then how much does the clock gain or loss in 22 hours?
2 minutes
20 minutes
120 minutes
1200 minutes
Sol : According to question, the Minute Hand overtakes hour Hand in 60 minutes. The Clock is faster than the usual.
We know that ,
5
65 ━ ─ Given Time
11
━━━━━━━━━━━ x Total Time
Given Time
5
65 ━ ─ 60
11
= ━━━━━━━━━━━ x 22 hours
60
5
5 ━─
11
= ━━━━━ x 22 hours
60
60
= ━━━━ x 22 hours
60 x 11
= 2 hours = 120 minutes Faster
Example : If in a clock the minute hand overtakes the hour hand in 70 minutes of correct time then how much does the clock gain or loss in 77 hours?
5 Hours Slow
5 Hours Fast
6 Hours Slow
6 Hours Fast
Sol : According to question, the Minute Hand overtakes hour Hand in 70 minutes. The Clock is slower than the usual.
We know that ,
5
65 ━ ─ Given Time
11
━━━━━━━━━━━ x Total Time
Given Time
5
65 ━ ─ 70
11
= ━━━━━━━━━ x 77 hours
70
6
4 ━─
11
= ━━━━━ x 77 hours
70
50
= ━━━━ x 77 hours
70 x 11
= 5 hours Slower
Type 2 : When clock is faster or slower by some minutes
Example : A clock which gains uniformly is 5 minutes slow on Sunday 5 PM if it is 7 minutes fast on Tuesday 5 PM then when was it correct ?
Monday 8 AM
Tuesday 8 AM
Monday 1 PM
Tuesday 1 PM
Sol : On Sunday 5 PM → 5 Minutes Slow
On Tuesday 5 PM → 7 Minutes Faster
We know that
Slow /Fast time
━━━━━━━━━ x Total Time
Slow + Fast Time
5
= ━━━ x 48 Hours [Sunday 5 PM to Tuesday 5 PM = 48 Hours]
12
= 5 x 4
= 20 Hours.
After 20 hours of Sunday 5 PM, Clock depicts Correct Time.
Hence, Sunday 5 PM + 20 Hours = Monday 1 PM
Example : A clock which gains uniformly is 8 minutes slow on Sunday 5 PM if it is 10 minutes fast on Wednesday 5 PM then when was it correct ?
Monday 8 AM
Tuesday 8 AM
Monday 1 PM
Tuesday 1 PM
Sol : On Sunday 5 PM → 8 Minutes Slow
On Wednesday 5 PM → 10 Minutes Faster
We know that
Slow /Fast time
━━━━━━━━━ x Total Time
Slow + Fast Time
8
= ━━━ x 72 Hours [Sunday 5 PM to Wednesday 5 PM = 72 Hours]
18
= 8 x 4
= 32 Hours.
After 32 hours of Sunday 5 PM, Clock depicts Correct Time.
Hence, Sunday 5 PM + 32 Hours = Tuesday 1 AM
Example : A clock which loss uniformly is 5 minutes fast on Sunday 5 PM if it is 7 minutes slow on Tuesday 5 PM then when was it correct ?
Sol : On Sunday 5 PM → 5 Minutes Fast
On Tuesday 5 PM → 7 Minutes Slow
We know that
Slow /Fast time
━━━━━━━━━ x Total Time
Slow + Fast Time
5
= ━━━ x 48 Hours [Sunday 5 PM to Tuesday 5 PM = 48 Hours]
12
= 5 x 4 Hours
= 20 hours
After 20 hours of Sunday 5 PM, Clock depicts Correct Time.
Hence, Sunday 5 PM + 20 Hours = Monday 1 PM
Example : A clock which loss uniformly is 5 minutes fast on Sunday 5 PM if it is 7 minutes slow on Monday 6 PM then when was it correct ?
Sol : On Sunday 5 PM → 5 Minutes Fast
On Monday 6 PM → 7 Minutes Slow
We know that
Slow /Fast time
━━━━━━━━━ x Total Time
Slow + Fast Time
5
= ━━━ x 25 Hours [Sunday 5 PM to Monday 6 PM = 25 Hours]
12
5
= 10 ━━━Hours
12
5
= 10 + ━━━ x 60
12
= 10 Hours 25 Minutes
After 10 Hours 25 Minutes of Sunday 5 PM, Clock depicts Correct Time.
Hence, Sunday 5 PM + 10 Hours 25 Minutes = Monday 3 : 25 AM
Example : A clock which loss uniformly is 9 minutes fast on Sunday 5 PM if it is 3 minutes slow on Wednesday 5 AM then when was it correct ?
Sol : On Sunday 5 PM → 9 Minutes Fast
On Wednesday 5 PM → 3 Minutes Slow
We know that
Slow /Fast time
━━━━━━━━━ x Total Time
Slow + Fast Time
9
= ━━━ x 60 Hours [Sunday 5 PM to Wednesday 5 PM = 60 Hours]
12
= 9 x 5 Hours
= 45 Hours
After 45 hours of Sunday 5 PM, Clock depicts Correct Time.
Hence, Sunday 5 PM + 45 Hours = Tuesday 2 PM
TYPE 3:
Example : A clock which gains 1 hour in every 24 hours is set right on Sunday 6 PM then what will be the actual time when the clock indicates Tuesday 8 PM ?
Sol :
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