In the competitive examinations, you will find questions in which you are asked to calculate the wages earned by the persons after doing some work. These types of questions come under the topic of Time and Work. The concept is very easy to understand and would be covered in this article.

Important Points:

(i) If a group of persons is doing a work with different efficiencies, then the person who has done the maximum work will get the maximum share of wages and the one who has done the least work will get least share of wages.

(ii) Sometimes instead of the work done, the efficiencies of the persons are given. So, the person who is most efficient will do the maximum work and will get the maximum share of the wages and the person who is least efficient will do minimum work and will get the least share of wages.

(iii) Mathematically, we have Wages Work done

Let us understand it with the help of an example:

Example:  A,B and C get an amount of Rs440 for their work. Together A and B are supposed to do of the work.How much does C get?

Solution:   A and B did and the remaining work was done by C i.e., C did of the work

As Wages ∝ Work done

So, C will get (iv) The second relation between the wages and the time taken to do the work is given by

Wages ∝ It means that wages are inversely proportional to the time taken to do that work. If an individual takes more time to do a particular work,he will get less wage and if he takes less time then he will get more wage.

Let us take an example:

Example: A can build a wall in 4 days and B can build in 6 days.The contract for the work is Rs 220. What will be their individual earnings?

Solution: As we know Wages ∝ Time taken by A =4 days

Time taken by B = 6 days

As wages are inversely proportional to time so the ratio of the wages of A and B is : =6:4 or 3: 2

So, A will get and B will get Now, to get thorough with the above concepts, let us practice some more questions.

EXERCISE:

Question 1: Suman can do a work in 3 days. Sumathi can do the same work in 2 days. They both finish the work together and get Rs. 150. What is the share of Suman?

(1) Rs. 30

(2) Rs. 60

(3) Rs. 70

(4) Rs. 75

Solution: (2)

Suman’s 1 day work = Sumati’s 1 day work = Ratio of Suman’s and Sumati’s 1 day’sWork = = 2 : 3

Suman’s share = × 150 = Rs. 60

Question 2: A and B undertook to do a piece of work for Rs. 4500. A alone could do it in 8 days and B alone in 12 days. With the assistance of C they finished the work in 4 days. Then C’s share of the money is

(1) Rs. 2250

(2) Rs. 1500

(3) Rs. 750

(4) Rs. 375

Solution: (3)

A’s 1 day’s work = B’s 1 day’s work = C’s 1 day work = Ratio of the work done by A, B and C is A: B: C = = 3: 2: 1

As Wages α Work done

C’s share = Rs. Question 3: If 6 persons working 8 hours a day earn Rs. 8400 per week, then 9 persons working 6 hours a day will earn per week.

(1) Rs. 8400

(2) Rs. 16800

(3) Rs. 9450

(4) Rs. 16200

Solution: (3)

Earning of 6 persons working 8 hours = Rs 8400

Earning of 6 persons per hour = 8400/8 = Rs 1050

Earning of 1 person per hour = 1050/6 = Rs 175

So, the earning of 9 persons working 6 hours = 175 × 9 × 6 = Rs 9450.

Question 4: A man and a boy received Rs. 800 as wages for 5 days for the work they did together. The man’s effi­ciency in the work was three times that of the boy. What are the daily wages of the boy?

(1) Rs. 76

(2) Rs. 56

(3) Rs. 44

(4) Rs. 40

Solution: (4)

Efficiency ∝ Efficiency of man: boy = 3:1

Ratio of time taken by man and boy = 1:3

Now wage∝ So, ratio in which wage will be given is 3:1.

Boy’s share = × 800= Rs. 200

The daily wages of boy=Rs. = Rs. 40

Question 5: A, B and C completed a work cost­ing Rs. 1,800. A worked for 6 days, B for 4 days and C for 9 days. If their daily wages are in the ratio of 5:6:4, how much amount will A receive?

(1) Rs. 800

(2) Rs. 600

(3) Rs. 900

(4) Rs. 750

Solution: (2)

Total Amount= amount given per day × total working days

Ratio of wages of A, B and C respectively

= 5 × 6: 6 × 4: 4 × 9

= 30: 24: 36 = 5: 4: 6

= × 1800

= × 1800 = Rs. 600

Question 6: A laborer was appointed by a contractor on the condition that he would be paid Rs. 75 for each day of his work but would be fined at the rate of Rs. 15 per day for his absence, apart from losing his wages. After 20 days, the contractor paid the laborer Rs. 1140. The number of daysthe laborer abstained from work was

(1) 3

(2) 5

(3) 4

(4) 2

Solution: (3)

Total salary for 20 days = Rs. (75 × 20)= Rs. 1500

Actual salary received = Rs. 1140

Difference = Rs. (1500 – 1140)= Rs. 360

Money deducted for 1 day’s absence from work = Fine+wage = Rs. (15 + 75) = Rs. 90

∴ Number of days labor abstained from work = = 4 days.

Question 7: If 5 men or 7 women can earn Rs. 5,250 per day, how much would 7 men and 13 women earn per day?

(1) Rs. 11,600

(2) Rs. 11,700

(3) Rs. 16,100

(4) Rs. 17,100

Solution: (4)

5 men =  7 women

∴   7 men = × 7 = women

So,7 men + 13 women= + 13 = women

Now, 7 women earn Rs. 5250

So, women earn = Rs. 17,100

Question 8: 2 men and 1 woman together can complete a piece of work in 14 days, while 4 women and 2 men together can do it in 8 days. If a man gets Rs.600 per day, how much should a woman get per day?

(1) Rs. 400

(2) Rs. 450

(3) Rs. 480

(4) Rs. 360

Solution: (1)

According to the question,

(2 × 14) men + 14 women= 16 men + 32 women

⇒ (28 – 16) men = (32 – 14) women

⇒ 12 men = 18 women

∴   1 woman = men

∴   Amount received by 1 woman per day.

= × 600 = Rs. 400

### Time and Work Questions: Problems on Time and Work you should solve for competitive examination preparation

Welcome to this exercise on Time and Work problems. In this exercise, we build on the basic concepts for Time and Work and explore the concept of wages. As you prepare for your competitive examinations, you will come across questions on wages. Such questions need optimized tackling and can be solved with ease by using simple tricks and understanding the relationships highlighted in this Time and WorkQuestions article. The Time and WorkQuestions and the wages questions exercise comes into the picture where it gives you a chance to practice the highlighted and important concepts related to thisTime and Workquestion type.

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