# Time and Work II- Time and Work Problems

### Efficiency based Time and Work problems are one of the most important kind of problems in IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC CGL, SSC CHSL and other competitive exams. This article will help you master a simple method to solve such problems in a just few seconds.

Time and work problems can help you boost your score in IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC CGL, SSC CHSL and other competitive exams, if you approach them the right away. In the first article in this series, we discussed time and work formulas that help you solve basic time and work problems. Moving forward on the same track, we will discuss time and work problems of the higher order that are often asked in SSC CGL, SBI PO and IBPS PO. So brace yourselves by revising the basic concepts and time and work formulas and get started for efficiency based time and work problems.

### What is Efficiency in Time and Work Problems?

In time and work problems efficiency is a key concept and generally refers to the amount of work done by an individual or a group of individuals in one day. In other words, you can say that time and work problems based on efficiency are actually about the capacity of individuals or group of people. Time and work problems based on this concept are not only a little complicated but also asked very frequently asked in competitive exams. So let’s establish a relation between terms and formulas that help to solve such time and work formulas.

### Relation b/w Terms to Solve Efficiency Based Time and Work Problems

The ideal and probably the best approach to solve such time and work problems is by unitary method where we fin d the work done in a unit day. The total work divided by the number of day will give us the work done in one day, which is also the capacity or the efficiency. So we can say that-
Let’s assume there are two individuals, ‘A’ and ‘B’ who are do the work in ‘a’ and ‘b’ number of days and we have to find how long would ‘A’ and ‘B’ take together to finish this work-
Also we know that number of people and number of days are inversely proportional to each other, which means that the more the number of people, the less time it will take to complete the work.
Also when two variables are inversely proportional, then direct additional is not possible. To solve time and work problems like these, we need two go by the capacity of the individuals. We know that the amount of work done by ‘A’ and ‘B’ in one day is-
Therefore we can say that the work finished by ‘A’ and ‘B’ in one day is-
We know that the number of days taken to complete the work and the work done in one day are actually reciprocal of each other. Therefore we can say number of days taken to complete the work and capacity are reciprocal of each other-
If there are three people, ‘A’, ‘B’ and ‘C’, then the total capacity of work done will be-
And when we reverse this, we get the total number of days taken to complete the work.

### Efficiency based Time and Work Problems-

Time and work problems discussed in this section are based on time and work formulas we have discussed above.

Problem 1: A, B and C, can finish a piece of work in 10, 15 and 30 days respectively. How many days will be required if A, B and C have to finish the work together?

Solution 1:
We can simply solve this time and work problem by substituting values in the formula for efficiency/capacity or add the individual efficiency of ‘A’, ‘B’ and ‘C’ t get their combined efficiency and then reciprocate it.
Step 1
Adding their individual efficiency, we get-
A + B + C = 1/10 + 1/15 + 1/30
A + B + C = 6/30
A + B + C = 1/5

Step 2
Reciprocating Efficiency to get No. of days, we get-
Time taken to Finish the Work = 5
Therefore, A, B, C will together take 6 days to finish the work.
Problem 2: B and C together finish the work in 8 days, A and B together finish the work in 12 days and A and C together finish the work in 16 days. In how many days together can A, B and C finish the work?
Solution 2:
The point worth noticing in time and work problems like this that efficiency are given in pairs. Such questions can be solved by slightly twisting the efficiency formula or just adding the efficiency in pairs and then working around it-
Step 1
Let’s look at the data we have-
B + C = 1/8     (i)
A + B = 1/12    (ii)
A + C = 1/16    (iii)

Step 2
Adding (i), (ii) and (iii) –
B + C + A + B + A + C = 1/8 + 1/12 + 1/16
2 (A + B + C) = 13/48
A + B + C = 13/96

Step 3
Reciprocating this to get the number of days-
No. of Days = 96/13 = 7 5⁄ 13
Therefore, A, B and C will together take 7 5⁄ 13 days to complete the work.

### Efficiency based Practice Time and Work Problems

Question 1:  A, B and C can finish a piece of work in 10, 15 and 30 days respectively. How many days will be required if A, B and C work together to finish the given work?
1) 5       2) 6       3) 7       4) 8       5) None of these
Question 2: Govind alone can complete a work in 20 days. Jagdish alone completes it in 30 days. How many days will be required if both of them work together?
1) 12 days       2) 24 days       3) 25 days       4)10 days       5) None of these

Do write your answers in the comments sections below and attempt time and work problems in practice test!