# Time and Work Shortcut Rules 4 to 6

Rule 4:
If A is twice as good a workman as B, then A will take half of the time taken by B to complete a piece of work.

Example

A is twice as good a workman as B. Together, they finish the work in 14 days. In how many days can it be done by each separately?
Sol:

Let’s assume that A alone can finish the work in x days.
It is given that A is twice as good a workman as B so B alone can finish the work in 2x days

So x = 21 days.
So A can finish the work in 21 days and B can finish the work in 42 days.

Rule 5:
If A is thrice as good a workman as B, then A will take one third of the time taken by B to complete a piece of work.

Example

A is thrice as good a workman as B. Together, they finish the work in 15 days. In how many days can it be done by each separately?
Sol:

Let’s assume that A alone can finish the work in x days.
It is given that A is thrice as good a workman as B so B alone can finish the work in 3x days.

So x = 20 days.
So A can finish the work in 20 days and B can finish the work in 60 days.

Rule 6:
If A and B together can do a piece of work in x days, B and C together can do in y days and C and A together can do in z days, then the same work can be done

Example

A and B can do a piece of work in 30 days while B and C can do the same work in 24 days and C and A in 20 days. Find out the time taken to complete the work by each member working alone. Also find in how many days they will complete the work if they work together.
Sol:

Here let’s assume that x=30, y=24 and z=20.