Clock - Quantitative Aptitude
Q1. At what angle the hands of a clock are inclined at 15 minutes past 5 ?
(a) 67 ½°
(b) 69 ½°
(c) 73 ½°
(d) 77 ½°
Answer: (a) 67 ½°
Angle traced by hour hand in 5h15 min
| = ( | 360 | X 5 + | 15 | )° |
| 12 | 60 |
= 157½°
Angle traced by min hand in 15 min = ((360/12) X 15)° = 90°
∴ Required angle = (157½)° - 90° = 67½°
Q2. A watch which gains uniformly is 2 minutes slow at noon on Monday and is 4 min 48 sec fast at 2 P.m. on the following Monday. When it was correct ?
(a) 6 PM Tuesday
(b) 12 PM Wednessday
(c) 2 PM Wednessday
(d) 4 PM Thursday
Answer: (c) 2 PM Wednessday
Time from 12 PM on Monday to 2 PM on the following Monday = 7 days 2 hours = 170 hours
The watch gains (2 + 44/5) min = 34/5 min
Now 34/5 min are gained in 170 hrs
∴ 2 min are gained in (170 X (5/34) X 2) hrs = 50 hrs
So the watch is correct 2 days 2 hrs after 12 PM on Monday
i.e it will be correct at 2 PM on Wednessday
Q3. At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together
(a) 53/11 min past 7
(b) 55/11 min past 7
(c) 57/11 min past 7
(d) 511/11 min past 7
Answer: (b) 55/11 min past 7
When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart
At 7 o'clock they are 25 minute spaces apart
∴ Minute hand will have to gain only 5 minute spaces
55 minute, spaces are gained in 60 minute
5 minute spaces are gained in ((60/55) X 5) min = 55/11 min
∴ Required time = 55/11 min past 7
Q4. The reflex angle between the hands of a clock at 10.25 is
(a) 197 ½°
(b) 198 ½°
(c) 201 ½°
(d) 203 ½°
Answer: (a) 197 ½°
Angle traced by hour hand in 125/12 hrs
| = ( | 360 | X | 125 | )° |
| 12 | 2 |
= 312 ½°
Angle trace by minute hand in 25 minute = (360/60) X 25° = 150°
∴ Reflex angle = 360° - (312½ - 150°) = 197 ½°
Practice Test Exam