If A can do a piece of work in n days, then A’s 1 day’s work = 1/n. The same concept is applied in case of pipes and cisterns. If a pipe takes n hours to fill a tank then in 1 hur it will fill 1/n part of tank and if a pipe can empty the tank in n hours then in 1 hour it will empty 1/n part of tank.
Inlet: A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.
Outlet: A pipe connected with a tank or a cistern or a reservoir, emptying it, is known as outlet.
If one pipe can fill tank in a hours and other can empty it in b hours then in 1 hour the tank will be filled or empty depends upon the value of a and b.
(1/a – 1/b ). If the calculation is –ve then tank will be empty and if calculation is +ve then the tank will be filled up.
If A is thrice as good a workman as B, then:
Ratio of work done by A and B = 3 : 1.
Ratio of times taken by A and B to finish a work = 1 : 3.
Speed = distance/time, Distance = speen x time
a km / hr = a × 5/18 m/s (To convert km/hr to m/s just multiply the quantity with 5/18 and to convert m/s to km/hr multiply the quantitiy by 18/5.
A man covers a certain distance at x km / hr and an equal distance at y km / hr. Then, the average speed is 2xy/(x + y)km/hr.
Average speed = Total Distance/total time
Formulas related to trains :
Time taken by a train of length ‘l’ metres to pass a pole or a standing man of a single post is equal to the time taken by the train to cover ‘l’ metres.
Time taken by a train of length ‘l’ metres to pass a stationary object of length ‘b’ metres is the time taken by the train to cove (l + b) metres.
Suppose two trains or two bodies are moving in the same direction at ‘u’ m /s and ‘v’ m /s, where u > v, then their relatives speed = (u – v) m / s.
Suppose two trains or two bodies are moving in the same direction at ‘u’ m /s and ‘v’ m /s, where u > v, then their relatives speed = (u + v) m / s.
If two trains of length a metres and b metres are moving in the opposite direction at ‘u’ m / s and ‘V’ m / s, then time taken by the trains to cross each other = (a + b)/ (u + v) sec.
If two trains of length a metres and b metres are moving in the same direction at u m / s and v m / s, then the time taken by the faster train to cross the slower train = (a + b)/ (u – v) sec.
If two trains (or bodies) start at the same time form points A and B towards each other and after crossing they takes a and b sec in reaching B and A respectively, then
A's Speed/B's Speed = √b : √a
Cases of Boats :
In water the direction along the stream is called downstream. And, the direction against the stream is called upstream.
If the speed of a boat in still water is u km / hr and the speed of the stream is v km / hr, then:
Down stream speed : ( u + v) km/hr
Upstream Speed : ( u – v) km/hr
If the speed downstream is a km / hr and the speed upstream is b km / hr, then:
Speed of boat in still water : (a + b)/2 km/hr
Speed of stream: (a – b)/2 km/hr