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**Efficiency based Time and Work problems are one of the most important kind of problems for competitive exams like SSC CGL and IBPS PO. 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 exams like SSC CGL, IBPS PO or SBI PO if you approach them the right away. In the first article on 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.

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**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!

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