Time & Work | How To Solve Problem Of Time & Work

Important Topic For RRB NTPC |TIME & WORK|

Let us study here some basic time and work concepts. In our daily lives, we come across so much work that needs to be completed within a specific time period.

Time and Work Concepts

Time and work problems solved with the simultaneous performance involving the efficiency of an individual and the time taken by them to complete a piece of work. Work is the effort applied to produce accomplish a task.

A fixed amount of time (T) is taken to complete a fixed work (W).

The number of units of work done per unit time is called the rate of work (R).


Hence,

Work (W) = Rate (R) X Time (T)

Some work is done, the total work itself can be taken as one unit. Hence, we assume the total work done as one unit in the problems we encounter in order to simplify the computations. In these cases,

Rate (R) = Work (W) Time (T)

Time (T) = Work (W) Rate (R)

We can say that Rate and Time are inversely proportional.

Basics formula of Time and Work:

Days = WorkEfficiency

In time and work, two types of questions asked in competitive exams ….

1). Homogeneous type.
2). Heterogeneous type.

Detail about homogeneous type:

M x D x T x E W = Constant

Where , M = Man Power, D = day T = Time, E = Efficiency

Practice Problems

TYPE 1:

Example: 24 men can do a piece of work in 12 days if they work 8 hours per day. Find the no. of days in which 36 men can do 6 hours?

Solution: with the help of this formula

M x D x T x E W = Constant

24 x 12 x 8 = 36 x D x 6
D = 24 x 12 x 836 x 6
D = 1023

Detail about heterogeneous type:

In this type of problems solved by two types methods :

1). LCM method:

In this method, we assume the total amount of work to be completed as the LCM of time taken by different people to complete the same piece of work.

Example: Ram can do a piece of work in 20 days and Mohan can do the same work in 30 days. Find the no. of days in which total work become complete if they work together?

Solution:

Ram =20 days
Mohan =30 days
Then, the LCM of 20,30 is 60
And, the efficiency of both are …
Efficiency of Ram = 60/20 =3,
Efficiency of Mohan = 60/30 =2
Total Efficiency =3+2 =5
Total days they completed the total work = 60/5 =12 days <here, 5 is the sum of the efficiency of ram & mohan>

NOTE:- WHEN THE EFFICIENCY IS GIVEN DIRECTLY, THESE PROBLEMS ARE CALLED “and and, and or” PROBLEMS.

Other Approach

1). Using Fractions

Ram can finish the work in 10 days i.e. in one day he will do 1/10th of the work.
Rahim can finish the work in 40 days i.e. in one day he will do 1/40th of the work.
So, in one day, both working together can finish= (1/10) + (1/40) = 5/40 = 1/8th of the work. So, to complete the work they will take 8 days.

1). Using Percentage (Shortcut Method)

Rahim can finish 100 % of work in 10 days i.e. in one day he finishes 10% of the work.
Ram can finish 100% of the work in 40 days i.e. in one day he finishes 2.5 % of the work.
So, working together, in a single day they can finish 12.5% of the work. So, to complete 100% of the work, they will take 100/12.5 = 8 days.

Point To Remember

• If A can do a piece of work in n days, then A’s one day’s work = 1/n
• If A’s one day’s work = 1/n, then A can finish the work in n days.
• If A is thrice as good a workman B, then
The ratio of work done by A and B = 3:1
The ratio of time taken by A and B to finish work = 1:3
• Total work = No of days * Efficiency.
• There are two groups of workers with same efficiency. In one group M1 workers can do W1 work in D1 days or time. In the second group M2 workers can do W2 work in D2 days or time.Then;

M1 D1 W2 = M2 D2 W1

Practise Problems Related To These Topic

Problem 1: A work twice as fast as B if both of them can together finish a piece of work in 12 days , then B alone can do it in days?

Solution: Ratio of efficiency of A and B = 2 : 1
Then, total work =12 x 3 = 36 <here, 5 is the sum of the efficiency of A & B>
B alone can do:: Days = 361 = 36 days

Problem 2. If 5 men or 9 women can do a piece of work in 19 days. In how many days 3 men and 6 women will do the same work?

Solution:
men |women | days
5 | 9 |19
3 | 6 | ?
5 men = 9 women

MenWomen = 95
Then, the ratio of men : women = 9 : 5
Days = 19 * 5 men/ 3 men + 6 women = 19*5(9)/3(9)+6(5) = 15 days

Problem 3:A is twice as efficient as C. B takes thrice as many days as A. C takes 12 days to finish the work alone. If they work in pairs (i.e., BC, AB, CA) starting with BC on the first day, AB on the second day and AC on the third day and so on, then how many days are required to finish the work?
Solution:
Time taken by C = 12 days
Time taken by B = 3 x 122 = 18days
Time taken by A = 122 = 6days
One days work of pair BC
= 112 + 118 = 536
One days work of pair AB
= 118 + 16 = 29
One days work of pair CA
= 16 + 112 = 14

First three days work = 536 + 29 + 14 = 1118
Next two days work (by BC and AB together)
= 536 + 29
= 1236
Remaining work after 5 days
= 1 – (1118 + 1236)
= 136
Required time = 3 + 2 + 436 = 519days

For more prblems related to this topic read Time And Work Problems

As you know, this topic is very important from a competition exam like RRB NTPC, SSC EXAM, etc. you can get help some other topics of mathematics from here. Here are some links which you may like:

  1. SHORT TRICK ROF FINDING SQUARE ROOT OF NON PERFECT SQUARE NUMBER
  2. SHORT TRICK ROF FINDING SQUARE OF ANY TWO DIGIT NUMBER
  3. SHORT TRICK OF MULTIPLICATION WITH 11
  4. NUMBER SYSTEM
  5. HOW TO PREPARE FOR RRB NTPC
  6. SHORT TRICK OF SQUARE OF THE NUMBER HAVING ITS LAST DIGIT 5

I hope this article will help you lot to understand various types of problems related to time & work chapter if you still have any doubt or any other problem related to this article you can ask it into the comment section. you will get a reply shortly.

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