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Two pipes can fill up a tank respectively in 3 hours and 6 hours and a third pipe can empty a tank in 9 hours. If three of them are working together then how long will it take to fill up the tank?
Tank filled in an hour when all of them are working simultaneously = 1/3 + 1/6 - 1/9 = 7/18
Hence time taken to fill up the tank = 18/7 h
Two taps A and B can fill a tank individually in 6 hours and 8 hours respectively and tap C can empty the same tank in 12 hours. If all the taps are kept open, how many hours would it take to fill the tank?
Let the volume of the tank = V
Let the efficiency of the tap A = V/A = V/6
And efficiency of the tap B = V/B = V/8
Efficiency of tap C to empty the tank = V/C = V/12
Let T be the total time taken by the system to fill the tank.
T*(V/6 + V/8 - V/ 12) = V
==> T = 24/5 = 4.8 hours.
So the correct option to choose is B - 4.8 hours.
Two persons A and B can complete a piece of work in 10 days and 20 days respectively. Together, they start working on the project, but A left after 4 days. How long more will B take to complete the project?
Let the total work be 200 units.
A’s rate of work = 200 units/10 days = 20 units per day
B’s rate of work = 200 units/20 days = 10 units per day
So, work done by A and B together in 4 days = (20+10)*4 = 120 units
Work left = 200 - 120 = 80 units
Time taken by B to complete the remaining work = 80 units/10 units per day = 8 days
A car covers a distance from town A to town B at the speed of 58 kmph and covers the distance from town B to town A at the speed of 52 kmph What is the approximate average speed of the car?
Let the distance between A and B be D.
Time taken = D/58 + D/52 = 110*D/(58*52)
So, average speed for the whole journey = 2D/Time = 58*52*2D/110D = 54.8363636 kmph = 55kmph approximately
A person travels the first 100km of his journey at 25km/hr and the next 200km at 40km/hr. Find the average speed of a person during his entire journey.
Average speed = (Total Distance travelled)/(Total time taken)
= (100+200)/(100/25 + 200/40) = 300/(4+5) = 100/3 = 33.33km/hr
Two trains A and B are going in the same direction with the speeds of 20 km/h and 15 km/h respectively. If the starting point of B is 200 km ahead from the starting point of A, how long will it take A to meet with the train B?
Relative speed of train A with respect to B = 5 km/h
Distance to be covered = 200 km
Time taken = $$\frac{200}{5}$$ = 40 h
A 400 m long train can cross a pole in 10 seconds. Find the time that this train will take to overtake a train of length 300m which is running at the speed of 72 km/hr in the same direction as that of the first train?
Let the speed of the first train be v m/s
Then
400/10 = v
=> v = 40 m/s
Now the speed of the second train = 72 km/hr = 20 m/s
Since both the trains are running in the same direction, the relative speed between the two trains is 40 - 20 = 20 m/s
Distance to be covered = 400 + 300 = 700m
Hence the required time = 700/20 = 35 seconds.
An empty tank has three inlet and two outlet pipes connected to it. An inlet pipe can fill an empty tank in 12 hours, while an outlet pipe can drain a filled tank in 10 hours. All inlet pipes have the same efficiency and both outlet pipes have the same efficiency. If all inlet pipes and outlet pipes connected to the empty tank are opened together, find the time in which the tank is completely filled.
Assume that the capacity of the tank is $$x$$ litres, the efficiency of an inlet pipe is $$y$$ litres per hour, and that of an outlet pipe is $$z$$ litres per hour.
So, given that an inlet pipe can fill an empty tank in 12 hours or,
$$\dfrac{x}{y}=12$$
$$y=\dfrac{x}{12}$$ . . . (1)
Also, given that an outlet pipe can drain a filled tank in 10 hours or,
$$\dfrac{x}{z}=10$$
$$z=\dfrac{x}{10}$$ . . . (2)
Now, all the pipes are opened together to an empty tank,
so the time taken to fill the tank is $$\dfrac{x}{3y-2z}$$
Putting the values of $$y$$ and $$z$$ from equations (1) and (2) we get
Time taken = $$\dfrac{x}{3y-2z}=\dfrac{x}{\dfrac{3x}{12}-\dfrac{2x}{10}}=20$$ hours
Hence, the answer is 20 hours.
A task is completed in a unique manner: on the first day, one man works; on the second day, two men work; on the third day, three men work, and so on, until the task is finished in 15 days. The same task is then assigned to women, who are known to be 40% as efficient as men. Following the same pattern, calculate the number of days required for the women to complete the task. (Round up to the nearest integer.)
It is said that the task was finished in 15 days, so if we assume that one man does one unit of work each day, the amount of work done by the men after n days can be found by the formula, $$\frac{n\left(n+1\right)}{2}$$
It is given that it takes them 15 days, substituting 15 for n in that formula, we get 120 units of work.
Now these 120 units are work done by men, it is given that women are 40% less efficient, that means $$0.4\left(M\right)=W$$
The same 120 units of men's work are equivalent to $$\frac{120}{0.4}=300\ units$$ of Women's work.
From the options we see, 24 days, which will equal $$\frac{24\left(25\right)}{2}=300$$
Hence, the answer is 24.
P, Q, and R can complete a task in 10, 15, and 20 days, respectively. P and Q start working on the task together, and after 3 days, R joins, and P leaves. If they work together for 3 more days, what fraction of the task is left to be completed?
Let the total work to be done is 300 units.
So, P does = 300/10 = 30 units per day
Q does = 300/15 = 20 units per day,
R does = 300/20 = 15 units per day.
P and Q start working on the take and worked for 3 days. So the work done in 3 days = (30 + 20)*3 = 150 units.
Now, R joins and P left. So, the work done by R and Q in the next 3 days = (20 + 15)*3 = 105 units
Remaining work = 300 - 150 - 105 = 45 units
Fraction of the work remaining = 45/300 = 3/20
Ravi and Raju started from a same point on a circular track in opposite direction. They met at 11 distinct points. Had they travelled in same direction they would have met at 5 distinct points. If Raju who is fastest amoung two, can travel 1200m in 15 sec, then in what time can Ravi travell the same distance?
Let us assume the speeds of Raju and Ravi as kx, ky.
The ratio of their speeds are x:y.
x+y = 11
x-y = 5
x = 8, y=3
We are given that Raju travels 1200m in 15 sec. His speed will be 80 m/s.
kx = 80 => k = 10.
The speed of Ravi is 30m/s.
Time Ravi takes to travel 1200m will be 40s.
Anuj and Bharat start running towards each other simulatenously, starting from points P and Q, respectively. They meet somewhere in between and continue on their journeys to Q and P, respectively. Anuj reaches Q 4 hours after meeting Bharat. Given that it took Anuj 10 hours to reach Q from P, how much time did Bharat take to reach P from Q?
Anuj took 4 hours after meeting Bharat. Hence, Anuj met Bhrat after 6 hours.
The time before their meeting can be calculated as $$\sqrt{\ t_1t_2}$$, where $$t_1$$ and $$t_2$$ are time taken by the two people to cover the remaining distance after crossing each other.
We get the equation $$6=\sqrt{\ 4t_B}$$
$$36=4t_B$$
$$t_B=9$$
Hence, it took Bharat 9 more hours after meeting Anuj to complete his journey and reach P.
This, in addition to the 6 hours before meeting Anuj, gives the total time taken by Bharat to be 15 hours.
Therefore, Option D is the correct answer.
A train takes 20 seconds to cross a pole. It crosses a platform 1000 meters long in 100 seconds. What is the train's speed?
Let the speed of the train be ‘v’ m/s and it’s length be ‘l’
Then
l/v = 20
20v = l
Also,
(l + 1000)/v = 100
=> 100v = 1000 + l
=> Solving both the equations, we get
v = 12.5 m/s and l = 250 m
Hence the length of the train is 250 m and speed = 12.5 m/s
A train starts from Mumbai towards Bengaluru at a speed of 80 kmph. After half an hour, another train from Bengaluru starts running towards Mumbai at a speed of 100 kmph. Find the distance travelled by the slower train when both the trains meet if the distance between Mumbai and Bengaluru is 940 kms.
In the first half an hour, the slower train covers some distance, which is
$$80\times\dfrac{30}{60}=40\ $$ km
Hence, now the distance between the two trains is $$940-40\ =900$$ km.
The time after which both trains meet is $$\dfrac{900}{80+100}=\dfrac{900}{180}=5$$ hrs
Hence, the distance travelled in this time by the slower train will be $$5\times80=400$$ km
But it also covered 40 km before this, so the total distance travelled is 40+400 = 440 km.
Hence, the answer is 440 km.
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