Sol : Option C
At 5 O’ clock, the two hands are 25 min spaces apart. In this case, the min hand will have to gain (25 + 8) i.e. 33 – minute spaces. So, 33 – minute spaces will be gained in (60/55)×33=36 min.
The hands will be 8 min apart at 36 min past 5.
Q.2. The minute hand of a clock overtakes the hour hand at intervals of 63 minutes of correct time. How many minutes in a day does the clock lose or gain?
A. 58(4/71)min
B. 54(6/81)min
C. 55(7/70)min
D. 56(8/77)min
Sol : Option D
In a correct clock, the minute hand gains 55 min spaces over the hour hand in 60 min.
To be together again, the minute hand must gain 60 min over the hour hand.
We know that 60 min are gained in (60/55)×60 = 65(5/11)min
But they are together after 63 min. gain in 63 min = 65 – 63 = 2 = 65(5/11) - 63=2(5/11) = (27/11)min.
Gain in 24 hrs = = 27×60×24/11×63 = 56(8/77)min.
Q.3. A watch which gains uniformly is 6 min slow at 5 p.m. on Monday. On the following Monday at 9 am, it was 10 min 40 seconds fast. When was it correct?
A. 8 : 36 pm. on Thursday
B. 2 : 36 am on Thursday
C. 2 : 36 pm. on Thursday
D. 8 : 36 am on Thursday
Sol : Option B
The clock has totally gained 16 minutes and 40 sec. i.e. 1000 seconds in 160 hrs. In order to show the right time, the clock has to gain only 6 min i.e. 360 seconds. Just apply the chain rule, the clock gained 1000 sec in 160 hrs, it will gain 360 sec. In 360 × 160/1000 = 288/5 hrs i.e. 57 3/5. Adding 57 hrs & 36 minutes in Monday 5 p.m. you get 2:36 a.m. on Thursday.
Q.4. At what angle are the hands of a clock inclined at 30 minutes past 8?
A. 95°
B. 75°
C. 92°
D. 97.5°
Sol : Option B
8: 30. Angle between 6 and 8 hour spaces is 30 × 2 = 60°. For additional 30 min, angle = 30 = 15°. Hence, required angle = 60 + 15 = 75°
Q.5. How many times are the hands of a clock at right angles in a span of twenty four hours?
A. 48 times
B. 44 times
C. 46 times
D. 22 times
Sol : Option B
In a span of 12 hrs, the hands of a clock are at right angles exactly 22 times. So, in a span of 24 hrs, they are at right angles exactly 44 times.
Q.6. How many times in a span of 24 hours are the hands of a clock straight (that is either overlap or exactly opposite to each other) ?
A. 43 times
B. 46 times
C. 45 times
D. 44 times
Sol : Option D
In a span of 24 hours, the hands of a clock are in opposite directions exactly 22 times & hands of a clock coincide exactly 22 times in a span of 24 hours. Therefore, they are straight 22 + 22 i.e. 44 times in a span of 24 hours.
Q.7. Find at what time between 7 o’clock and 8 o’clock will the hands of a clock be in the same straight line but not overlap each other.
A. 10(9/11) min past 8
B. 5(5/11) min past 7
C. 10(8/11) min past 8
D. 10(7/11) min past 8
Sol : Option D
Between 7 and 8, the hands will be in opposite directions at (5 7 – 30)(12/11) = 60/11 min. i.e.5(5/11) min past 7.
Q8. When the hands of a clock show 4 o’clock, the angle between them is
A. 100°
B. 120°
C. 130°
D. 150°
Sol : Option B
Required angle will be 30 4 = 120°, because between 12 and 5 there are 4 hours and each hour = 30°.
Q9. In one and half hours, the minute hand of a clock rotates through an angle of
A. 720°
B. 540°
C. 600°
D. 420°
Sol : Option B
In one and half hours, the minute hand of a clock rotates through an angle of 1.5 360 = 540.
Q10. A clock is set right at 10 a.m. on Monday. The clock loses 15 min. in 24 hrs. What will be the true time when the clock indicates 4 am on the following Saturday?
A. 5:12 am
B. 5:32 am
C. 6:32 am
D. 5:48 am
Sol : Option A
From 10 am on 1st day to 4 am on 5th day is total 114 hours. When a clock loses 15 min, then 23 hours 45 min of this clock are the same as 24 hours of correct clock i.e. 95/4 hours of this clock = 24 hours of correct clock. 95/4 hours of this clock =((24×4/95)×114) hours of correct clock = 115.2 hours of correct clock which is equal to 115 hours 12 minThe correct time is 5:12 am.
-icon.jpg?null&itok=2FjKP8-O "Chain Rule Practice Problems"){kind=icon}
