83. 
At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together? 


C
In one hour,once minute hand and hour hand comes in straight line
so our answer is something 7 past,not 8 past
use formula,
titha(0)=30h11/2m
titha is 180,hour hand is on 7
put values
we get titha=60/11
convert into quotitent*remainder/divisor format
we get
5*5/11So answer is 5*5/11 past 7.
82. 
A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is: 


Error Clock :: Original Clock
3 min 5 sec :: 3 min
185 sec :: 180 sec
[9 hr 15 min = 555 min = 33300 sec]
33300 sec :: (180/185 x 33300) sec
33300 sec :: 32400 sec
333000sec = 9 hrs 15 min :: 32400 sec = 9 hrs [:. 32400/3600 = 9]
So,
Time passed by Error clock = 9 hrs 15 min.
Time passed by Original clock = 9 hrs.Therefore, 9 hrs after 7 am is 4 pm.
81. 
A clock is started at noon. By 10 minutes past 5, the hour hand has turned through: 


Initially both hands are at 12(noon)
1 hr= 30 dgrs ( 12 to 5 = 5 hrs)
so 5*30 = 150 dgrs and
in 60 mins cover 30 dgrs
in 10 mins= 30/60
in 1 min= 30/60*10= 5 dgrs
so
150 + 5 = 155 dgrs
80. 
An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? 


Clock is consider as circle 360 deg
the duration of Time= 6 hrs
total = 12 hrs
calculated deg=time duration*deg/total hrs
=6(360/12)=180
79. 
A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank? 


Let A fill tank in x hrs.
Therefore tank filled in one hrs is 1/x.
And B pipe is twice than A means 2 (1/x).
C pipe is twice than B means 2 (2 (1/x) ) i.e 4/x.
1/x+2/x+4/x = 1/5.
7/x = 1/5.
x = 35 hrs.
78. 
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is: 


Let the capacity of tank x gallons. then in 1 minute tank filled (x/20+x/243)gallons
From the question we can write
15(x/20+x/243)=x [it took 15 min to fill x gallons]
x/20+x/24x/15=3
(6x+5x8x)/120=3
3x/120=3
x=120 gallons
77. 
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is: 


2nd pipe is 5 hours faster than 1st.so 2nd pipe=5x
1st pipe automatically takes 1 hour to fill the tank.1st pipe=1x.
in question 2nd pipe is 4 hours slower than 3rd pipe.
i.e 5x+4x=9x
3rd pipe =9x
add all 3 pipes i.e 1x+5x+9x=15.
76. 
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in: 


If the total area of pump=1 part
The pumop take 2 hrs to fill 1 part
The pumop take1 hour to fill 1/2 portion
Due to lickage
The pumop take 7/3 hrs to fill 1 part
The pumop take1 hour to fill 3/7 portion
Now the difference of area = (1/23/7)=1/14
This 1/14 part of water drains in 1 hour
Total area=1 part of water drains in (1x14/1)hours= 14 hours
So the leak can drain all the water of the tank in 14 hours.
75. 
Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is: 


Now study the problem carefully the given data is
two trains moving in opposite direction . that means we add them 100+100=200mtsto cross these 200mts it takes 8 secs ok
now, they have asked to find the speed of the faster train if the speed is twice the slower train , this is given in the question.Now ,
speed=distance/time
speed=200mts/8secs ok
as options are given in km/hr , we have to convert speed to km/hrSo we multiply with 18/5
well (200mts/8secs)*18/5=(200/8)*(18/5)=90km/hr
these is the total speed .Now they asked us to find the speed of the train twice the other train
Let the speed of first train =xkm/hr
Speed of other train should be twice=2x km/hr
So we have got total speed as 90km/hr
x+2x=90km/hr
3x=90km/hr
x=30km/hr
speed of one train is 30km/hr.So they asked twice the speed of train
So we get 2x=2*30
=60km/hr
Now if we add 30+60=90km/hrWe got the total speed
The speed of the faster train is 60 km/hr
74. 
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train? 


Here they given train speed=72kmph now convert into m/s that is 72*5/18=20m/s.
And time 26sec given. This time taken by the train to cross the total platform.
So now we know train speed, and time. Speed=distance/time.
Distance=speed*time=20*26=520m.
So this is total distance of platform and train. i.e (platform+train length).
Platform+Train length=520.
250+Train length=520.
Train length=520250=270m.