A convenient way to solve problems on the efficiency and ratios is to use the concept of efficiency and ratios. In the following section, we will see efficiency ratio and how we can solve all the problems on the concepts of time and work by the use of this technique. Let us see!

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## Efficiency Ratio – Work and Time

### Ratio

If A is thrice as good a workman as B, then:

The ratio of work done by A and B = 3: 1.

The ratio of times taken by A and B to finish a work = 1 : 3. This means that if someone says A is ‘x’ times as good a workman as B, then he will take the time to B to do the same work.

**Browse more Topics under Work And Time**

### Efficiency

The efficiency of work means, “How much work one person can do in one day (expressed in percentage)”. For example, a person can do a job in 2 days. In other words, we can say that he can do 50% of the work in one day. Therefore, his efficiency will be 50%.

The following two steps can be followed to better utilise the concept of efficiency. This concept involves two steps to calculate efficiency:

Step 1: Convert the work into fraction i.e. per day work.

Step 2: Express the fraction in the form of percentage by multiplying with 100. Let us see this with the help of an example.

Example 1: If a person can complete his work in 5 days. What will be his efficiency?

Answer: Number of days a person takes to complete his work = 5 days.

This means that he is doing 1/5 th of the work per day (Step one – convert into fraction).

Now let us do the second step and convert it into a percentage:

We have: 100/5 = 20%. Therefore, the person’s efficiency is 20%. Summarizing this, we can say that if a person can do his job in n days, his efficiency will be given as below:

Efficiency =(100/n) %.

*Let us understand more about Work from Days here in detail *

### Negative And Positive Efficiency

Now the efficiency can be negative as well as positive. For example, if we have a man who builds a wall in 10 days, his efficiency will be equal to (100/10)% = 10%. Suppose we also have another man who is demolishing the same wall. he can demolish the entire wall in two days. Therefore his efficiency will be – (100/2)% = – 50%.

Negative efficiency cancels the positive efficiency.

Another Example: Positive efficiency = 5%, Negative efficiency = 1.5%. Therefore the Net efficiency = (5 – 1.5)% = 3.5%.

The efficiency cancels out only when the work is of the same nature.

## Solved Examples For You

Example 2: A can do a job in 10 days. B can do a job in 5 days. In how many days they can complete the job if they work together?

Answer: Since A can do the job in 10 days, we can write the efficiency of A is equal to (100/10)% = 10%. Thus, A’s efficiency = 10%. Similarly, we can say that B’s efficiency is equal to 20%. Now we nee to find their combined efficiency as follows:

(A+ B) efficiency = (10 + 20)% = 30%. This means in one day A and B together can do 30% of the work. Therefore, Number of days A and B together take to do 100% of work = (100/3) days = 3.33 days.

Example 3: A can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?

Answer: Ratio of time taken by A & B = 160:100 = 8:5. Suppose B alone takes x days to do the job. Then, 8:5::12:x. In other words, we may write: 8x = 5×12 and thus we have x = 15/2 days.

Example 4: If eight men and 12 boys can complete a piece of work in twelve days, in what time will 40 men and 45 boys complete another piece of work three times as great, supposing sixteen men can do as much work in 8 hours as 12 boys can do in 24 hours? [SSC Mains, 2003]

A) 4 days B) 16 days C) 8 days D) 32 days

Answer: We are given that sixteen men can do a certain work in 8 hours. The same amount of work can be done by 12 boys in 24 hours.

We can write 16 = 1/8 and 12 = 1/24.

Therefore we can write the two equations as (16 men)×(8 hours) = 1 [ 1 means the complete 100% of work].

Similarly, we can say that (12 boys)×(24 hours) = 1. Comparing the two equations, we can write (16 men)×(8 hours) = (12 boys)×(24 hours).

On the left-hand side, we have the men and on the right-hand side, we have the boys. So we can write (16 × 8 hours) men = (12 × 24) boys. In other words, we may write, 4 men = 9 boys which means that the amount of work that 4 men can do could be done by 9 boys.

Therefore, moving on to the question, we have: 8 men + 12 boys can do some work in 12 days. Converting the equation to boys only, we have:

8 men + 12 boys = 9 × 2 boys + 12 boys = 30 boys.

Similalry, from the second condition in the question, we have: 40 men + 45 boys = 10 × 9 boys + 45 boys = 135 boys.

Now, 30 boys can complete the work in 12 days. This means that one boy can complete the work in 30×12 days. Therefore, 135 boys will complete the work in (30×12)/135 days.

Also, the number of boys that will complete the work three times bigger = (30×12×3)/135 = 8 days. Therefore the answer is C) 8 days.

*Practice Work and Time Questions here*

## Practice Questions:

Q 1: A and B together can do a job in 4 days. If A can do a job in 12 days if he works alone, then how many days B alone take to complete the job?

A) 6 days B) 8 days C) 10 days D) 10 days

Ans: 6 days.

Q 2: Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

A) 4: 7 B) 7: 3 C) 4: 3 D) 3: 7

Ans: C) 4: 3

This concludes our discussion on the topic efficiency ratio.