Quantitative Aptitude Notes Part 10( Time and work)

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

  1. Time taken single piece of work, If A Persondo a piece of work or job in n days, then person’s finish the work in n days = 1 / n.
  2. A person does a piece of work inday = 1 / n, then person can finish the work in n
  3. If A person twicework a workman as B person, then Ratio of work done by A and B is = 2 : 1.
  4. 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
  5. 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.

Example:
20 labors can do piece of work in 30 days, then how many days 15 laborcan complete double of the work?
Answer:
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.

 

Example:
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?
Answer:
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.

Examples:
Jagat painted a wall in 6 days of 12 hours each and Pradumnpainted the same wall in 8 days of 8 hours each. How long will they work ifworking together 36 / 17 hours a day?
Answer: 
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.AndPradumn’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.

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

Example:
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?
Answer:
6 women work done a piece of work in 10 days and 10 children done it 15 days
Step 1: So 6 women x 10 days = 10 children x 15 days
= 2women = 5 children
Step 2:10children x ? = 6 w x 10
? =6 days

 

Example:
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?
Answer: 
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.

 

Example:
The works of wall paint of ratio Amit & Vikas is 3 : 5. If Amit and Vikasworktogether in 30 days,in how many days Vikas alone can paint a complete wall?
Answer:
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.

 

Example:
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 .

 

 

 

 

 

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