71. Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
Answer: 9 min
Explanation:Work done by third tap in 1 min = (1/18-1/10+1/15) = -10/90 = -1/9 (The negative value denote that emptying)
so the third tap alone can empty the cistern in 9 min.
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72. Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Answer: 17 1/7 min
Explanation:Cistern part filled by pipe A in 1 min = 1/20
and by pipe B in 1 min = 1/30
Pipe C empty cistern in 1 min = 1/40 part.
When all pipes are open Cistern part will be filed = (1/20+1/30-1/40) = 7/120
=> Time required to fill the cistern = 120/7 = 17 1/7 min.
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73. Two pipes A and B can fill a tank in 9 hours and 3 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours will the tank be full?
Answer: 5 hrs
Explanation:Tank part filled by pipe A in 1 hour =1/9
Tank part filled by pipe B in 1 hour =1/3
Given Pipe A and B are opened alternatively.
So Part filled in every 2 hours =(1/9+1/3)=4/9
Tank Part will be filled in 4 hour =2*4/9=8/9
Remaining part = (1-8/9)=1/9
So next is A turn.
So Pipe A will fill remaining 1/9 part in next 1 hour.
Total Time = (4 hrs + 1 hrs) = 5 hrs.
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74. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
Answer: 79.2 km/hr
Explanation:Let the length of the train be x meters and its speed by y m/sec.
Then, x/y = 8 => x = 8y ----------- (1)
As per the question total distance = (x + 264) meters.
(x + 264)/20 = y
Put the value of x from equation 1.
=> 8y + 264 = 20y
=> y = 22.
Therefore Speed = 22 m/sec = ( 22 x 18 /5) km/hr = 79.2 km/hr.
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75. Two trains 400m and 300m long run at the speeds of 50 kmph and 40kmph respectively in opposite Directions on parallel tracks. The time taken to cross each other?
Answer: 28 secs
Explanation:Trains are running in opposite Direction:
So need to find Length of two Trains = 300m + 400m = 700m
and Total Speed = 40 Kmph + 50 Kmph (Opposite Direction)
= 90 Kmph
so speed (m/sec) = 90 * 5/18 m/sec = 25 m/sec
Formula Used: Time = Distance/Speed
Time = 700/ 25 sec
Time = 28 Sec
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76. A car covers four successive 6 km stretches at speeds of 25 kmph, 50 kmph, 75 kmph and 150 kmph respectively. Its average speed over this distance is
Answer: 50 kmph
Explanation:Time = Distance/Speed
Time taken for each 6 km can be given by
6/25, 6/50, 6/75 and 6/150
Total time = (6/25) + (6/50) + (6/75) + (6/150) = (36 + 18 + 12 + 6)/150 = 72/150
Average speed = Distance/time = (24/72) x 150 = 50 kmph
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77. Albert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
Answer: 12 kmph
Explanation:Let's Assume the distance travelled Albert = x km.
Formula Used: Time = Distance/Speed
so (x/10 - x/15) = 2 hrs
=> (3x - 2x)/30 = 2 hrs.
=> (3x - 2x) = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 hrs = 6 hrs.
Formula Used: Speed = Distance/Time
So, Albert started 6 hours before 2 P.M. i.e @ 8 A.M.
Required speed = 60/5 kmph. = 12 kmph.
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78. The sum of the ages of a mother and her son is 45 years. Five years ago, the product of their ages was 3 times the mother age at that time, then the present age of the son,
Answer: 8
Explanation:Given
Let's assume mother age = x years. ----- (1)
sum of mother and her son age = 45
so son age will be = (45-x) years. ------- (2)
Five year ago:
mother age will be = (x-5) years
son age will be = (45-x-x) years = (40-x) year.
As per question
(x-5) * (40-x) = 3*(x-5)
=> (40-x) = 3
=> x = 37 year.
so son age will be (45-37) = 8 years.
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79. A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only. Then, C alone can do the job in :
Answer: 9 3/5
Explanation:1 day's work done by A = 1/16
1 day's work done by B = 1/12
1 day's work done by (A, B and C) = 1/4
=> so C 1 day's work = (1/4-1/12-1/16) = (12/48-4/48-3/48) = 5/48
so C alone can do the work = 48/5 days = 9 3/5 days
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80. A can finish a piece work in 18 days and B can do the same work in half the time taken by A. So if they working together, what part of the same work can finished in a day?
Answer: 1/6
Explanation:First find the 1 day work of both (A & B)
A's 1 day's work = 1/18
and
B's 1 day's work = 1/9 (B can do work in half time)
(A + B)'s 1 day's work = (1/18+1/9)
= (1+2)/18 = 3/18 = 1/6
so A & B together can do 1/6 of work in 1 day.
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