Time and Work and Shortcuts

In Real life we come across practical problems of accomplishing the given project in prescribed time limit. Since the efficiency of different person is different, thus proper note have to be taken.

THEORY 

Let a person A can finish a task in x days and person B finish in y days , then

A can finish 1/x part of work in one day and

B can finish 1/y part of work in one day.

If both work together to finish the task then they can finish as  in one day and days together

Considering in Cases. 

Case 1. Working together

Example 1-

A can finish task in 8 days and B can finish the same in 10 days. How many days are required to finish the task if both are working together.

Solution

A does work in 8 days and thus in one day 1/8 parts

B does work in 10 days and thus in one day 1/10 parts

total work done together in one day is 1/8+1/10 = 9/40 parts

thus 40/9 days needed to do work together i.e. 4 days 4 hrs.

Case 2. Working in Alternate Days

Example 2

Let A can finish the task in 8 days and B can finish the same in 10 days. How many days are required if both are working in alternate days.

Case 2.a- Consider Work Starting from A

Solution

A does work in 8 days and thus in one day 1/8 parts

B does work in 10 days and thus in one day 1/10 parts

Since both are working alternately starting from A , then first 2 days work would be 1/8+1/10 parts, i.e 1st Day A finish 1/8 part and 2nd Day B finish 1/10 part = 8+10/80 =18/80  -----> eqn (1)

From eqn(1) we can tell that total parts of work is 80 .

They both continued to work till 8th day i.e 72/80 parts of work is done , and still 8/80 parts of work is left.

which is to be finished by A on 9th day so, to finish 1/10 part A needs 1/10/1/8 = 4/5

So together they can finish work in 8 days 1 Hr and 20 Minutes.

Case 2.b- Consider Work Starting from B

Solution

A does work in 8 days and thus in one day 1/8 parts

B does work in 10 days and thus in one day 1/10 parts

Since both are working alternately starting from B ,then first 2 days work would be 1/10+1/8 parts, i.e 1st Day A finish 1/8 part and 2nd Day B finish 1/10 part = 10+8/80 =18/80  -----> eqn (1)

From eqn(1) we can tell that total parts of work is 80 .

They both continued to work till 8th day i.e 72/80 parts of work is done , and still 8/80 parts of work is left.

which is to be finished by B on 9th day so, to finish 1/10 part A needs 1/10/1/10 = 1 day

So together they can finish work in 8+1 days = 9 days.

Case 3. Concept of Man , Day, Hour

These are few concepts of Time and Work.

                                                                      Thank-You!