## Time and Work Notes

# 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

### Practice questions on Time and Work

**Theory:**

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

= 1/X+1/Y-1/Z

So time taken to fill the tank by all three

= (XYZ)/(XY-YZ-XZ)

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