Work from Days section will ask you questions in which you will have to calculate the amount of work that we can perform in some time. In a similar manner to the concept of days from work, the work from days section is easily solved by the application of some basic concepts and the formulae that we will develop. Here we have solved examples and all the important concepts that you may have to answer while solving this section. Let us see.

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## Work from Days

Let us start by developing the formula for this section.

First, we have the formula of the work. Where work is the numerical value of the task. Work = Number of days (Time) (T or D) × Number of men (M). In other words, W = D × M.

Suppose w_{1} is the work done in the first case and w_{2} in the second case. Also, let us suppose that T_{1} is the number of days that the first person takes and T_{2} is the number of days that the second term takes. Also, let N_{1} and N_{2} represent the number of people that undertake each task respectively. Then the ratio of the work done in the first task to the work done in the second task is equal to w_{1}/w_{2} = (T_{1} × N_{1})/(T_{2} × N_{2}). Let us see some examples of getting work from days.

### Solved Example

Example 1: Ten people can cut 20 trees in 2 days. If twenty people work for two months, then how many trees will be cut during this time?

A) 1330 trees B) 1223 trees C) 1220 trees D) 1222 trees

Answer: We will use the formula w_{1}/w_{2} = (T_{1} × N_{1})/(T_{2} × N_{2}) that we have developed just above. Here w_{1 }= 20, T_{1} = 2 and N_{1} = 10.

Similarly, we have w_{2} = ? , T_{2} = 61 days, and N_{2} = 20. Substituting these values in the equation above, we have:

w_{1}/w_{2} = (T_{1} × N_{1})/(T_{2} × N_{2}). In other words we can say: 20/w_{2} = (2×10)/(61×20).

Solving this we can say that w_{2} = 1220 trees.

We can use the same formula to solve similar questions. Let us now see an important concept that will simplify a lot of our problems. The concept of efficiency in work. Hence the correct option is C) 1220 trees.

## Efficiency Of Work

The efficiency is the amount of work that a person can do in some certain time. For example, consider the following example:

Example 2: What is the efficiency of a person who finishes his job in 5 days?

Answer: As per the question, the number of days this person takes to complete the work = 5

Therefore we can say that he does 1/5th of the work per day. This when we convert it into percentage = 100/5 = 20%. Therefore, his efficiency is 20%.

We can use the efficiency to solve many problems in a very short time. Let us see how.

Example 3: A person ‘A’ can do a job in 10 days. Another person ‘B’ can do the same job in 5 days. In how many days will they complete this job if they work together?

Answer: As per the question, we have A’s efficiency = 10% and B’s efficiency = 20%.

Therefore when they work together, their efficiency is = A+ B = 10 + 20 = 30%

This means, in one day A and B together can do 30% of work. Therefore, the number of days it will take A and B together to do 100% of the work = 100/30 = 3.33 days.

## Some Solved Examples

Example 4: A and B can do a job in 8 days. B and C can do the same job in 12 days. When A, B, and C work together, they can do the same job in 6 days. In how many days can A and C complete this job?

Answer: As per the question we have:

The combined efficiency of A and B is = (A+B’s) efficiency = 12.5%

Also, we have: B+C’s efficiency = 8.33%

And A+B+C’s efficiency = 16.66%

Now we need to find A + C. Let us see how to solve this:

Consider, the expression 2(A+B+C), we can write it as = (A+B) + (B+C) + (C+A)

Therefore we have 2(16.66) = 12.5+ 8.33 + (C+A)

And hence we have: C+A = 12.49 = 12.5%

Therefore, the time that A and C take = 100/12.5 = 8 days.

Example 5: A person A is twice as efficient as another person B. The person A can complete a job 30 days before B. If they work together, how long will it take them to finish the job?

Answer: Let the efficiency of B = x and thus the efficiency of A = 2x.

Since the person A takes 30 days to complete a job, the person B will take 60 days to complete the same job.

A’s efficiency = 1/30 = 3.33%

B’s efficiency = 1/60 = 1.66%

Therefore there combined efficiency for this job = 3.33% + 1.66% = 5% of the job in 1 day.

So they can complete the whole job in 20 days (= 100/5 days).

## Practice Questions

Q 1: A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 30 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone?

A) 3:1 B) 3:2 C) 1:3 D) 2:3

Ans: C) 1:3

Q 2: A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

A) 37 (1/2) B) 36 C) 39 (1/2) D) 40

Ans: 37 (1/2)