# Work And Wages

If you want to get a government job in any sector, then Work And Wages is a very important topic in the Quantitative Aptitude section. For students appearing in competitive exams, we have brought here Work and Wages Formulas for your practice, which will help you to solve the Work And Wages Questions asked in the upcoming examinations. Also, here we are giving a PDF of Work And Wages Question in Hindi for your convenience. Candidates can also check Work and Wages Formulas, Work and Wages Shortcut Tricks to solve questions in a detailed way from this page.

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## Work And Wages

Work And Wages Formula

1) Total Wage = Total number of days × Wage of 1 day of a person

Example: If Arjun’s monthly wage is Rs 4200 and he worked for 30 days, then his daily wage is calculated as

4200 = 30 × Wage of 1 day of a person (Daily Wage)

Daily Wage = 4200/30 = Rs 140

2) Wage is directly proportional to the work done. It means, more money is received for more work and less money is received for less work.

3) Wage is indirectly proportional to the time taken by the individual.

4) Wage is directly proportional to 1 day work of each individual.

Example: If Karan can do a piece of work in 10 days and Arjun can do the same piece of work in 15 days.

Then, ratio of Karan and Arjun’s wage will be 15:10 = 3:2

5) If A and B can do a piece of work in x and y days respectively, the ratio of their wages will be y:x. Then

the wages earned by A and B will be:

Wage of A = Total wages × y/(x + y)

Wage of B = Total wages × x/(x + y)

Basics Principles Of Work And Wages

To solve the questions related to work and wages, it is necessary to pay attention to the following main points.

• When the ratio between work done by two or more persons is the ratio of their wages.
• When two or more persons have the same working day, then the ratio between their work of 1 day is the ratio of their wages.
• When a person works, his wages are in proportion to the work done by him while the time taken by him to work is inversely proportional to his wages.
• The more work a person does, the higher his wages will be.
• The more time a person takes to work, the less his wages will be.

Work And Wages Shortcut Tricks

Trick – 1

A can do a work in x days and B can do the same work in y days. If the contract for the work is Rs.X, and both of them work together, then the share of A and B is given by Trick – 2

A,B and C can do a work in x,y and z days respectively. If doing that work together they get an amount of Rs. X, then the Trick – 3

A person A can do a work in x days. With the help of a another person B , he can do the same work in y days. If they get Rs. X for that work, then the share of A and B is given by Trick – 4

A, B and C contract a work for Rs.X. If together A and B are supposed to do xy of the work, then the share of C is given by Trick -5

x1 men and y1 boys can earn Rs. X1 in d1 days, if x2 men and y2 boys can earn Rs.X2 in d2 days, then the following relationship is obtained, Trick -6

A and B undertake to do a work for Rs.X. A can do it alone in x days and B in y days. If with the assistance of a boy they finish the work in ‘d’ days, then the share that

A gets is ,

B gets is and

the Boy gets is Rs.X[1−(x+yxy)d]

And the ratio of shares is given by A:B; Boy = dy:dx:xy – d (x+y)

Problems on Work and Wages

Question 1: Ram and Shyam undertake a piece of work for Rs 300. Ram can do it in 20 days and Shaym can do it in 60 days. With the help of Radha, they finish it in 10 days. How much should Radha be paid for her contribution?

Solution:

Ram alone takes 20 days and Shyam alone takes 60 days to finish the work.

All together can finish in 10 days.

Let the total work done is LCM (10, 20, 60) = 60

Ram’s efficiency = 60/20 = 3

Shyam’s efficiency = 60/60 = 1

Combined Efficiency = 60/10= 6

Radha’s efficiency = 6 – 3 -1 = 2

Radha contributed 1/3 of the total work done.

So, she should be paid 1/3 of the total amount = 300/3 = Rs 100

Question 2: A can do a piece of work in 30 days. He works only for 5 days and left, then B finishes the remaining work in 15 more days. In how many days will A and B together finish the work?

Solution:

25 days work of A completed by B in 15 days.

25A=15B

A/B=3/5

A’s efficiency = 3

B’s efficiency = 5

Total work done= 3 * 30 = 90

Work done by A and B together=total work done/total efficiency

= 90/8

= 11.25 days

Question 3: Twenty five employees can finish a project in 40 days.After how many days should 10 employees leave the job so that the project is finished in 50 days.

Solution:

Let n be the number of days when 10 employees left the project.

Total work done= 25*40= 1000

25x + (50 – x)15 = 1000

25x + 750 – 15x = 1000

10x = 250

x = 25

Hence, after 25 days 10 employees left the job.

Question 4: A can type 85 pages in 10 hours. A and B together can type 500 pages in 40 hours. How much time B will take to type 80 pages.

Solution:

A can type 85 pages in 10 hours

Then, A can type 340 pages in 40 hours.

A and B together can type 500 pages in 40 hours

So, B can type number of pages= 500 – 340 = 160 pages in 40 hours.

Hence, B can type 80 pages in 20 hours.

Question 5: A, B and C can do a piece of work in 10, 12 and 15 days respectively.They all start the work together but A leaves after the 2 days of work and B leaves 3 days before the work is completed.Find the number of days the work completed.

Solution:

Total work done is LCM(10, 12, 15)=60 unit

A’s efficiency = 60/10= 6

B’s efficiency = 60/12= 5

C’s efficiency = 60/15= 4

First two days all work together

So, the work completed in first two days= 15 x 2 = 30 unit

Remaining work= 60 – 30 = 30 unit

If B completes 3 day work also = 3 x 5 = 15 unit

Total work remaining= 30 + 15 = 45 unit

Number of days B and C works= 45/9=5

Total number of days to complete the work = 2 + 5 = 7 days.

Question 6: Two friends A and B were employed to do a work. Initial deadline was fixed at 24 days. Both started working together but after 20 days, A left the work and the whole work took 30 days to complete. In how much time can B alone can do the work?

Solution:

Let the total work be 24 units. It is given that A and B together can do the work in 24 days.

=> Combined efficiency of A and B = 24/24 = 1 unit / day

=> Work done in 20 days = 20 units

=> Work left = 24 – 20 = 4 units

Now, this remaining 4 units of work was done by B alone in 10 days.

=> Efficiency of B = 4/10 = 0.4

Therefore, time required by B alone to do the work = 24/0.4 = 60 days

Question 7: A and B took a job to be completed in 20 days. They started working together and after 12 days, C joined them and the whole job finished in 15 days. How much time would C require to complete the job if only C was hired?

Solution:

Let the total job be 20 units. It is given that A and B took the job to be completed in 20 days.

=> Combined efficiency of A and B = 20/20 = 1 unit / day

Now, job done in 12 days = 12 units

=> Job Left = 8 units

Now, this remaining 8 units of job has been done by all A, B and C together.

Let the efficiency of C be ‘x’.

=> Combined efficiency of A, B and C = 1+x units/ day

Now, with this efficiency, the job got completed in 3 more days.

=> Job done in 3 days = 3 x (1+x) = 8 units

=> x = 5/3

Therefore, efficiency of C = x = 5/3 units / day

Hence, time required by C alone to do the job = 20/(5/3) = 12 days

Question 8: Three people A, B and C working individually can finish a job in 10, 12 and 20 days respectively. They decided to work together but after 2 days, A left the work and after another one day, B also left work. If they got two lacs collectively for the entire work, find the difference of the highest and lowest share.

Solution:

Let the total work be LCM(10, 12, 20) = 60 units

=> Efficiency of A = 60/10 = 6 units / day

=> Efficiency of B = 60/12 = 5 units / day

=> Efficiency of C = 60/20 = 3 units / day

Since the number of working days are different for each person, the share of each will be calculated in the ratio of the units of work done.

Now, A works for 2 days and B works for 3 days.

=> Work done by A = 2 x 6 = 12 units

=> Work done by B = 3 x 5 = 15 units

=> Work done by C = 60 – 12 – 15 = 33 units

Therefore, ratio of work done = 12:15:33 = 4:5:11

So, A’s share = (4/20) x 2,00,000 = Rs 40,000

B’s share = (5/20) x 2,00,000 = Rs 50,000

C’s share = (11/20) x 2,00,000 = Rs 1,10,000

Therefore, difference of the highest and lowest share = Rs 1,10,000 – 40,000 = Rs 70,000.

Question 9: Three friends A, B and C are employed to make pastries in a bakery. Working individually, they can make 60, 30 and 40 pastries respectively in an hour. They decided to work together but due to lack of resources, they had to work on shifts of 30 minutes. Find the time taken to make 185 pastries.

Solution:

It is given that A, B and C make 60, 30 and 40 pastries respectively in an hour.

=> In 30 minutes, they will make 30, 15 and 20 pastries respectively.

So, in one cycle of 1 hour 30 minutes where each works for 30 minutes, pastries made = 30 + 15 + 20 = 65

Now, in 2 cycles (3 hours), 130 pastries would be made.

In the next 30 minutes, A would make 30 pastries.

So, total time elapsed = 3 hours 30 minutes and pastries made = 130 + 30 = 160

In the next 30 minutes, B would make 15 pastries.

So, total time elapsed = 4 hours and pastries made = 160 + 15 = 175

In the next 15 minutes, C would make 10 pastries.

So, total time elapsed = 4 hours 15 minutes and pastries made = 175 + 10 = 185

Therefore, total time taken = 4 hours 15 minutes.

Question 10: A can do 1/6 work in 4 days and B can do 1/5 of the same work in 6 days. In how many days both will finish the work?

Solution:

A can complete the work in 6*4 = 24 days

B can complete the work in 5*6 = 30 days

Total work done LCM(24, 30)= 120 unit

A’s efficiency = 120/24= 5

B’s efficiency = 120/30= 4

Total time taken = total work done/ total efficiency

= 120/9

= 40/3 days

Question 11: A company undertake a project to build 2000 m long bridge in 400 days and hire 50 men for the project. After 100 days, he finds only 400 m of bridge has been completed.Find the (approx )number of extra men he hire to complete the project on time.

Solution:

Use here M1 D1 / W1 = M2 D2 / W2

50 x 100/ 400 = [(50 + x) 300]/ 1600

4 x 5000 = 15000 + 300x

20000 – 15000 = 300x

3x = 50

x= 16.66

x =17 men to hire to complete the project on time.

Question 12: In a hostel mess there was sufficient food for 400 students for 31 days of a month. After 26 days 150 students go to their home. For how many extra days will the rest of food last for the remaining students.

Solution:

After 26 days food left in mess= 5 * 400

Students remaining in hostel mess =400 – 150 = 250

Let x be the extra days.

5 * 400 = (5 + x ) * 250

2000 = 1250 + 250x

250x = 750

x = 3 days

Hence, food will last for 3 extra days.

Question 13: Two candles A and B of same height can burn completely in 6 hours and 8 hours respectively. If both start at same time with their respective constant speed, then calculate after how much time the ratio of their height will become 3:4.

Solution:

Total time is LCM (6, 8) =24

A’s efficiency = 24/6 = 4

B’s efficiency = 24/8= 3

After x time height will become 3:4

So, (24 – 4x) /( 24 – 3x) = 3/4

96 – 16x = 72 – 9x

7x = 24

x = 24/7 = 3.42 hours

Question 14: A and B men can build a wall in 20 and 30 hours respectively but if they work together they use 220 less bricks per hour and build the wall in 15 hours. Find the number of bricks in the wall.

Solution:

Work done is LCM(20, 30) = 60

A’s efficiency= 60/20 = 3

B’s efficiency= 60/30 = 2

If they work together their efficiency will be 5.

Working together their efficiency 60/15 = 4

Efficiency is less than by 5 – 4 = 1

1 -> 220 less bricks

60 -> 220 x 60 = 13200 bricks in the wall.

Question 15: A start a work and left after 2 days and remaining work is done by B in 9 days. If A left after 3 days then B complete the remaining work in 6 days. Then in how many days A and B can complete the work individually.

Solution:

Work done is equal in both cases.

2A + 9B = 3A + 6B

A=3B

A/B=3/1

Total work done =3 x 2 + 9 x 1

= 15

A alone take 15/3 = 5 days.

B alone take 15/1 = 15 days.