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Time ,work,speed, distance

  1. 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. 

  1. 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.

  1. Speed = distance/time, Distance = speen x time

  2. 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.

  3. 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 :

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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 :

  1. In water the direction along the stream is called downstream. And, the direction against the stream is called upstream.

  2. 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

  1. 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