Clock Reasoning Questions – Hard Level

Q-31. The minute hand of a clock overtakes the hour hand at intervals of 66 minute of correct time. How much a day does the clock gain or lose?
(a) 11\frac{109}{121} minute gain

(b) 11\frac{109}{121} minute loss

(c) 11\frac{117}{121} minute gain

(d) 11\frac{117}{121} minute loss

View Answer and Solution 

Answer: (b) 11\frac{109}{121} minute loss
Solution:
Total loses in 66 minutes is
= 66 - 65 \frac{5}{11}
= 66- \frac{720}{11}
= \frac{726 - 720}{11} = \frac{6}{11}
In 1 minutes
=\frac{6}{11\times 6}
In 24 × 60 Minute
=\frac{6\times 24\times 60}{11\times 6}
= \frac{1440}{121}
=11 \frac{109}{121}minutes loss
 

Q-32. A clock is set right at 8 a.m. on sunday. It gains 8 minutes in 24 houus. What is the correct time when the clock indicates 9 p.m. on upcoming sunday?
(a) 9 P.M (b) 8:30 P.M
(c) 8 P.M (d) 10 P.M

View Answer and Solution 

Answer: (c) 8 P.M
Solution:
Total hours form 8 a.m. Sunday to 9 p.m. following sunday = 181 hours
24 hours + 8 minutes
24+\frac{8}{60}= 24+\frac{2}{15}
= \frac{360+2}{15}  hours
\frac{362}{15}hours of this clock
⇒ 24 hours of correct clock
1 hours of this clock = 24 ×\frac{15}{362}hour of correct clock
181 hour of this clock
=\frac{24\times 15\times 181}{362}
=180 hours of correct clock
The correct time would be:
9pm - 1 hour = 8p.m
 

Q-33. A clock is set right at 10 A.M on sunday. It loses 8 minutes in 24 hours. What is the correct time when the clock indicates 9 P.M on next sunday?
(a) 9 P.M (b) 9 A.M
(c) 10 A.M (d) 10 P.M

View Answer and Solution 

Answer: (d) 10 P.M
Solution:
Total hours of clock from 10 - A.M Sunday to 9 P.M on following Sunday = 179 hours
24 hour - 8 minutes = 23 hour 52 minutes
23+\frac{52}{60}
= \frac{345+13}{15}= \frac{358}{15} hr.
\frac{358}{15} hours of this clock = 24 hour of correct clock
1 hour of this clock = 24 ×\frac{15}{358}hour of correct clock
179 hour of this clock
=\frac{24\times 15\times 179}{358}
= 180 hour of correct clock.
The correct time would be = 9
p.m. +1 hour = 10 p.m.
 

Q-34. A watch which gains uniformaly is 4 minute slow at 9 A.M on Sunday, and is 4 minute 15 sec. fast at 9P.M on upcoming Friday. When was it correct?
(a) 2 A.M Thursday (b) 6 P.M Wednesday
(c) 1 A.M Wednesday (d) 6P.M

View Answer and Solution 

Answer: (c) 1 A.M Wednesday
Solution:
Sunday 9 A. M
Upcoming Friday 9 P.M
= 4 minute 4 Minute 15 sec.
Total gains = 8 min 15 sec
=8+\frac{15}{60}
= 8+\frac{1}{4}
=\frac{33}{4}min
Total hours = 5 days + 12 hr.
= 120 + 12 = 132 hours
\frac{33}{4} min. gains in = 132 hour
1 minute gains in
= \frac{132}{33} x 4
4 minute gain in
= \frac{132}{33} x 4 x 4 = 64 hour
9 A.M Sunday + 64 hours
9 A.M Sunday + 2 dyas 16 hours = 1 A.M Wednesday
 

Q-35. A watch which loses uniformaly is 3 minute fast at 6 A.M on Thursday and is 3 minute 12 sec. slow at 5 P.M on upcoming wednesday. When was it correct?
(a) 9 P.M on Sunday
(b) 9 A.M on Monday
(c) 9 A.M on Sunday
(d) 8 A.M on Sunday

View Answer and Solution 

Answer: (c) 9 A.M on Sunday
Solution:
6 A.M Thursday 5 P.M upcorning Wednesday +3 minutes - (3 minutes + 12 sec.)
Total loses = 6 min. + 12 sec
=6+\frac{12}{60}
= 6+\frac{1}{5}
=\frac{31}{5}min
Total hour = 6 days + 11hour
=24×6+11=144+11=155 hour
\frac{31}{5}minutes lose in = 155 hr.
1 minutes lose in = \frac{155}{31} x 5
3 minutes lose in = \frac{155}{31} x 5 x 3
= 75 hour
75 hour = 3 day + 3 hour
So, Thursday 6 A.M+ (3 day +3 hour)
= Sunday 9 A.M