# How to solve Time & Work (Shortcut Approach)

By Jyoti Bisht|Updated : March 8th, 2022

How to solve Time & Work: Time and work are essential topics in a variety of competitive exams, including banking and insurance exams. A thorough understanding of this subject will undoubtedly aid you in passing the exam with flying colors. Learn how to solve time and work concerns using the formula and some quick tips.

Questions about time and labor are provided below, along with answers. The time and work problems form the basis for a number of other ideas, such as data interpretation and data sufficiency. Here we will help you understand the use of the Work Constant approach.

While attempting questions, you must remember some important points -

1. Read the questions carefully.

2. Words like together, alone, before complete, after complete, etc. are important.

3. Data provided in the question should be read carefully.

How to approach and express data while taking the exam?

If there are two-person A and B. If A begins and both work alternate days. It means

 1st day 2nd day 3rd day 4th day 5thday 6thday 7thday 8thday 9thday 10thday ….. A B A B A B A B A B …..

Before going forward, we will discuss some basics of Ratios to make calculation easy for this topic and these basics will also help you in other topics like Partnership, time and distance, average, allegation, etc.  TIME AND WORK EXAMPLES:

Example 5: A and B can do work in 8 days and 12 days respectively.

A                B

Time (T)         8 days      12 days

Efficiency (η)     12             8

η             3               2

total work  = TA× η= TB× ηB
total work =  8 × 3 =  12 × 2
total work = 24 units

(a). If both A and B work alternatively and  A begins, then in how many days work will be completed?

According to the question, A begins and both and b work alternately.

 Days 1st day 2nd day 3rd day 4th day 5th day 6th day 7th day 8th day 9th day 10th /2-day total TotalWork Person A B A B A B A B A B Work Unit 3 2 3 2 3 2 3 2 3 1 24

Hence work will be completed in 9 (1/2) days.

But this type of approach is not helpful in exams. We will go by basic but in a smarter way.

If we make a pair of A and B, we can say that both together will work 5 units but in 2 days.

2 days = 5 units of work

2 days × 4 = 5 units of work × 4

8 Days   = 20 units of work, i.e. we can say that up to the 8th day 20 units of work will be done

But on the 9th day, it’s a chance of A and he will do his 3 units of work. So up to the 9th day, 23 units of work will be done. Now 1 unit of work will remain. On the 10th day, it’s a chance of B.

As above B does 2 units of work in a day. So, he will do 1 unit of work in (1/2) days.

So total time taken to complete the work is 9 (1/2) days.

(b). If A and B both work for 4 days then A leaves. In how many days total work will be completed.

(EffA+B× tA+B )+( Eff.B × TBB) = total work
(5 × 4)+(2 ×TBB) = 24
20 + 2 × to= 24
2 ×toB = 4
tB = 2 days , hence total time will be ( 4+2 )days i.e. 6 days.

Important: The same question can be framed in many ways.

Way 1: B works for 2 days and after that A joins B, then in how many days the work will be completed.

Solution: B works only for 2 days and then A joins B, i.e. both will work together after 2 days.
(BB × ηB) + (tA+B× ηA+B) = total work
(2 × 2) + (tA+B × 5) = 24
(tA+B × 5) = 20
tA+B  = 4 days   hence total time is (2+4) days i.e. 6 days

Way 2: A and B both work together and A takes leaves for 2 days, then in how many days the work will be completed.

Solution:  When both A and B are working together and A takes leaves for two days it means B has to work alone for 2 days

Let total time to complete the work is t days.

So,  η­A+B × (t-2) + ηB × 2 days = 24
5 × (t-2) + 2 × 2 = 24
t-2 = 4
t = 6 days Hence total time taken to complete the work is 6 days.

Don’t confuse between tA+B and TA+B  (as mentioned in the article1). Both are different.

Example 6: X can do work in 6 days, Y can do it in 8 days and Z can do it in 12 days.

(a). If X starts the work and X, Y, Z works on alternate days, then in how many days the work will be completed?

Solution: Here X will start work on the 1st  day, then Y will work on the 2nd day, and z will work on the 3rd day.

X:   Y:  Z
Time           6 :   8  : 12

Efficiency    12 × 8: 6 × 12 : 8 × 6

η               96 :  72 : 48
η                 4 :  3  :  2

total work = ηX× TX= ηY×TY Z×TZ

total work = 6 × 4 = 8 × 3 = 12 × 2 = 24 units

On 1st day, work done by X = 4 unit

On 2nd day, work done by Y = 3 unit

On 3rd day, work done by Z = 2 unit

Total work in 3 days done by X,Y and Z = 9 unit

Now again X will come then Y, then Z and so on till work is completed.

In 3 days   =    9 units

× 2           × 2

In 6 days    =   18 units

X will work on 7th day   = 4 units

=  22 units

Now we need (24-22) units = 2 units work more but Y can do 3 units of work in one day. So 2 units will be done in (2/3) day.

+(2/3) day          + 2 unit

Total days=7 (2/3) days       24 units

Hence total work will be done in 7 (2/3) days.

(b). If all started together and after completion of (3/4)the work, Y left and remaining work is done by X and Z together. Then in how many days work will be completed?

Solution: Total work is 24 units then (3/4)the work is 18 units.

One day work of (X+Y+Z) = 9 units so in 2 days 18 units of work will be done by (X+Y+Z) together.

After this Y left, X+Z worked together and 6 units of work remained.
One day work of X+Z = (4+2) units = 6 units. So in 3 days, total work will be completed.

Now, that you are clear with the concept, do attempt the quiz to make sure that you have understood it properly.

You can also go through the Part - I of Time and Work series from the link below -

### How to solve Time & Work (Shortcut Approach) - Part I

This is an important chapter for the following exams:

 S. No. Name of the exam 1 SBI Clerk 2 3 IBPS Clerk 4 IBPS PO 5 6 RBI Assistant 7 8 10 12

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## FAQs

• Solve time and work questions for bank exams 2022: We examine the principles and formulas for time and work before moving on to solving questions concerning time and work. If 'M1' people can accomplish 'W1' work in 'D1' days and 'M2' people can do 'W2' work in 'D2' days, then the relationship M1 D1 W2 = M2 D2 W1 has a very unusual general formula.

• The candidates can practice the time and work questions at BYJU'S EXAM PREP for improvising their speed and accuracy.

• Here are the tips to solve time and work questions for bank exam-

1. Pay close attention to the questions.
2. Words like "together," "alone," "before completion," "after completion," and others are crucial.
3. The information supplied in the question should be carefully studied.
• Here is the list of bank exams 2022 in which you will be getting the time and work questions: SBI Clerk, SBI PO, IBPS Clerk, IBPS PO, IBPS RRB, RBI Grade-B, NABARD Grade-A, SBI Apprentice, LIC AAO, RBI Assistant

### PO, Clerk, SO, Insurance

BankingIBPS POIBPS ClerkSBI POIBPS SOSBI ClerkRBIIDBI SOIBPS RRBLICESICNainital BankOtherQuick LinkMock Test GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com