Ans .
\(47*1/2^{\circ}\)
angle traced by the hour hand in 12 hours = \(360^{\circ}\)
Angle traced by it in three hours 25 min (ie) 41/12 hrs=\((360*41/12*12)^{\circ}\)
=\(102*1/2^{\circ}\)
angle traced by minute hand in 60 min. = \(360^{\circ}\).
Angle traced by it in 25 min. = (360 X 25 )/60= \(150^{\circ}\)
Required angle = 1500 -102*\(1/2^{\circ}\)= 47*\(1/2^{\circ}\)
Ans .
120/11 min. past 2
At 2 o'clock, the hour hand is at 2 and the minute hand is at 12, i.e. they
are 10 min spaces apart.
To be together, the minute hand must gain 10 minutes over the hour hand.
Now, 55 minutes are gained by it in 60 min.
10 minutes will be gained in (60 x 10)/55 min. = 120/11 min.
The hands will coincide at 120/11 min. past 2.
Ans .
paste right option
At 4 o'clock, the minute hand will be 20 min. spaces behind the hour hand,
Now, when the two hands are at right angles, they are 15 min. spaces apart. So,
they are at right angles in following two cases.
Case I. When minute hand is 15 min. spaces behind the hour hand:
In this case min. hand will have to gain (20 - 15) = 5 minute spaces. 55 min. spaces are gained by it in 60 min.
5 min spaces will be gained by it in 60*5/55 min=60/11min.
They are at right angles at 60/11min. past 4.
Case II. When the minute hand is 15 min. spaces ahead of the hour hand:
To be in this position, the minute hand will have to gain (20 + 15) = 35 minute spa' 55 min. spaces are gained in 60 min.
35 min spaces are gained in (60 x 35)/55 min =40/11
They are at right angles at 40/11 min. past 4
Ans .
120/11 min
At 8 o'clock, the hour hand is at 8 and the minute hand is at 12, i.e. the two
hands_ are 20 min. spaces apart.
To be in the same straight line but not together they will be 30 minute spaces apart.
So, the minute hand will have to gain (30 - 20) = 10 minute spaces over the hour hand.
55 minute spaces are gained. in 60 min.
10 minute spaces will be gained in (60 x 10)/55 min. = 120/11min.
The hands will be in the same straight line but not together at 120/11 min.
Ans .
346/11 min. past 5
At 5 o'clock, the minute hand is 25 min. spaces behind the hour hand.
Case I. Minute hand is 3 min. spaces behind the hour hand.
In this case, the minute hand has to gain' (25 - 3) = 22 minute spaces. 55 min. are
gained in 60 min.
22 min. are gaineg in (60*22)/55min. = 24 min.
The hands will be 3 min. apart at 24 min. past 5.
Case II. Minute hand is 3 min. spaces ahead of the hour hand.
In this case, the minute hand has to gain (25 + 3) = 28 minute spaces. 55 min. are gained in 60 min.
28 min. are gained in (60 x 28_)/55=346/11
The hands will be 3 min. apart at 346/11 min. past 5.
Ans .
440/43 minutes
In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.
To be together again, the minute hand must gain 60 minutes over the hour hand. 55 min. are gained in 60 min.
60 min are gained in (60/55) x 60 min =720/11 min.
But, they are together after 65 min.
Gain in 65 min =720/11-65 =5/11min.
Gain in 24 hours =(5/11 * (60*24)/65)min =440/43
The clock gains 440/43 minutes in 24 hours.
Ans .
Wednesday
Time from 8 a.m. on Sunday to 8 p.m. on following Sunday = 7 days 12 hours = 180 hours
The watch gains (5 + 29/5) min. or 54/5 min. in 180 hrs.
Now 54/5 min. are gained in 180 hrs.
5 min. are gained in (180 x 5/54 x 5) hrs. = 83 hrs 20 min. = 3 days 11 hrs 20 min.
Watch is correct 3 days 11 hrs 20 min. after 8 a.m. of Sunday.
It will be correct at 20 min. past 7 p.m. on Wednesday
Ans .
11 p.m
Time from 5 a.m. on a day to 10 p.m. on 4th day = 89 hours.
Now 23 hrs 44 min. of this clock = 24 hours of correct clock.
356/15 hrs of this clock = 24 hours of correct clock.
89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock.
= 90 hrs of correct clock.
So, the correct time is 11 p.m.
Ans .
48 min. past 12
Time from 8 a.m. on a day 1 p.m. on the following day = 29 hours.
24 hours 10 min. of this clock = 24 hours of the correct clock.
145 /6 hrs of this clock = 24 hrs of the correct clock
29 hrs of this clock = (24 x 6/145 x 29) hrs of the correct clock
= 28 hrs 48 min. of correct clock
The correct time is 28 hrs 48 min. after 8 a.m.
This is 48 min. past 12.