Time and work

What is work? 
Work is the quantity of energy transferred from one system to another but for question based on this topic; Work is defined as the amount of job assigned or the amount of job actually done.

Some Important Formula
Time taken single piece of work, If A Person do a piece of work or job in n days, then person’s finish the work in n days = 1 / n.
A person does a piece of work in 1 day = 1 / n, then person can finish the work in n days.
If A person twice work a workman as B person, then Ratio of work done by A and B is = 2 : 1.
The reciprocal of day work gives the alone time i.e., alone time ( or time to complete a job  by a single person) =  1 / 1 day’s work
When more than one person working on the same type of work, then there combined work = sum of 1 day work by each person. Suppose P, Q, R work same piece of work by each person (P + Q + R)”s 1 day’s work = P’s day’s work + Q ’s day’s work + R’s day’s work.


20 labors can do piece of work in 30 days, then how many days 15 labor can complete double of the work?

20 labor can do a piece of work in 30 days and Now we need to find the double of the work by 15 labor.
We use
=> (labor  working days) = (labor  working days)
= 20 x 30 = 15 x ?
= 600 = 15 x?
? = 600 / 15 = 40
now we need to double the working days is 40 x 2 = 80 days.

Sameer and Karan can do a piece of work in 20 days and 12 days respectively. Sameer started the work alone and then after 4 days Karan joined him till the completion of the work. How long did the work last?

Step 1:  In 4 days Sameer work done = 1 x 4 / 20 = 1 / 5.
              and Remaining work is = (1 – 1 / 5) = 4 / 5.
Step 2: Now Sameer and Karan work done by 1 day= (1 / 20 + 1 / 12) = 2 / 15.
Step 3:4 / 5 work will be done by Sameer and Karan = (15 / 2 x 4 / 5) = 6 days.
So the total time taken = (6 + 4) = 10 days.

Jagat painted a wall in 6 days of 12 hours each and Pradumn painted the same wall in 8 days of 8 hours each. How long will they work if working together 36 / 17 hours a day?

Step 1: At first we find total work of both per day 12 hours than 6 day he total work (6 x 12) = 72      hours. And Pradumn’s total work is (8 x 8) = 64 hours.

Step 2: both 1 hour’s work is 1 / 72, 1 / 64.So Both together work in 1 hour’s is ( 1 / 72 + 1 / 64 ) = 17 / 576 hour’s.

Both finish the work 576 / 17 hour’s.

Step 3: number of days of 36 / 17 each = (576 / 17 X 17 / 36) = 16 days.
So Both together works in 16 days.

30 children can complete a piece of work in 50 days. In how many days 15 children can complete the same piece of work?
we use (children x working days) = (children x working days)
30 x 50 = 15 x ?
1500 = 15 x ?
?  = 100 days.

6 women alone can complete a piece of work in 10 days, whereas 10 children alone take 15 days to complete the-same piece of work. How many days will 6 women and 10 children together take to complete the piece of work?
1/10+1+15=1/6 ,So work complete in 6 days

Rahul can complete a job in 16 days and Manish can complete equal job in 18 days, some reason Manish work for 9 days and left the job. Now in how many days Rahul can complete the remaining job?

Step 1: Manish complete the job in 9 day that is (1 / 18 X 9) = 1 / 2.So remaining work is (1 – 1 / 2) = 1 / 2.
Step 2: Now Rahul complete its work in (1 / 16 X 2) = 8 days.
So Rahul complete the work in 8 days.


The works of wall paint of ratio Amit & Vikas is 3 : 5. If Amit and Vikas work together in 30 days, in how many days Vikas alone can paint a complete wall?
We know the ration of Amit and Vikas is 3 : 5
So Amit + Vikas  together work done by in 30 days.
Amit + Vikas = 30 x 15 = 450 work
So, Vikas alone work done by = 450 / 5 = 90 days.
Now Vikas alone can work of paint a wall completed in 90 days.


20 boy are required to complete a work in 100 days .how many boys are required to complete that work in 5 days?
Answer:
Number of  boys required = 20 x 100 / 5 = 400
So , 400 boy required to complete that work in 5 days .