TIME AND WORK
In any organization the efficiency of different person is different; the management has to take proper note of it before distributing the task to subordinates. We discuss all such Problems under the heading Time and work.
- When time is constant (T = Constant)
Person ‘P’ is directly proportional to work. It means mare work requires more number of persons.
- When work is constant (w = Constant)
Work ‘W’ is proportional to Time it means more work requires more time.
- When work is constant.(W= Constant)
Number of persons ‘P’ is inversely proportional to time. It means more person will takes less time.
with the above three relations between P, T and W we find that
Let a Person A finish a work in X days then
One day work of A is =1/X
And a person B can do a work in y days then
One day work of B is =1/Y
If both A and B are working together then
One day work is =1/X +1/Y = (X+Y)/XY
Now time taken by A and B to complete the whole work =XY/(X+Y)
Work and Wages:
A can do a certain piece of work in X days and B in Y days both of them work together to do the work. If the total paid of the work is Rs. M then each would get –
Ratio of time taken is =X:Y
As we know that –
Efficiency α 1/Time
So the ratio of efficiency = Y:X
Here money will divide to according to their efficiency then
A’s share =X/(X+Y)
And B’s share = X/(X+Y)
PIPES AND CISTERN:
Pipes are connected to a tank or cistern and are used to fill or empty the tank.
Inlet Pipe: A pipe used to fill the tank or cistern is known as Inlet Pipe.
Outlet Pipe: A pipe used to empty the tank or cistern is known as Outlet Pipe
If a inlet A can fill the tank in X hours.
The part of the tank filled in 1 hour = 1/x
And inlet B can fill the tank in Y hours
The part of tank filled in 1 hour =1/Y
If both pipes are opened together then part filled in 1 hour = 1/X + 1/y
Rule: If a pipe fills a tank in X hours and another fills the same tank in Y hours , but a third empties the full tank in Z hours and all of them are opened together, the net part filled in 1 hour is
So time taken to fill the tank by all three