Time and work concept of Work and Wages with solved examples(using shortcut methods).

Work and Wages:

These types of questions are d in competitive exams sometimes. In these questions, we have to find out the wages of workers based on their work efficiency and the amount of work done by them. 

The basic principle of finding time and work remains but additionally, we need to find the Wages to be given to the employee.

To solve these questions, I am going to use the concept of ratio and proportion, and partnership.

To understand questions you need to understand how to find time and work.

Refer to the following posts if you are new:

Time and work concept of Efficiency, LCM method, Man-Day hour formula method.

Examples Based on Work and Wages.

Ex 1. Suman can do work in 3 days. Sumati can do the same work in 2 days. Both of them finish the work together and get 150 Rs. what is the share of suman?

Sol. The ratio of work efficiency of suman and Sumati is 3:2

The ratio of time efficiency of suman and Sumati is 2:3

Both of them together finish 5 work

5 = 150

1 = 30

Suman's share 2 = 60Rs.

Sumati's share 3 = 90 Rs.

Ex.2 A and B undertook to do a piece of work for 4500 Rs. An alone could do it in 8 days. B alone can do it in 12 days. With the assistance of C, they finished the work in 4 days then C's share of the money is?

Sol. A = 8 , B= 12 , A+B+C = 4

LCM of 8,12 and 4 is = 24

One day work of

A =24/8 = 3

B = 24/12 = 2

A+B+C = 24/4 = 6

A+B+C = 6

Put the value of A+B in the above equation

5+C = 6

C = 1

Ratio of A,B,C is 3:2:1

3+2+1 = 6

6= 4500 Rs.

1 = 750 Rs.

Thus C's share is 750 Rs.

Ex.3 If 6 persons working 8 hours a day earn 8400 Rs. per week then 9 people working 6 hours a day will earn per week?

Sol. we will use the man-day-hour formula method

MDH/W = MDH/W

M= man

D= day

H= Hour

W=wages

Let us suppose x is the wage of 9 people working 6 hours

(6*8)/8400 = (6*9)/x

x = 9450 Rs. Ans

Ex 4. A man and a boy reviewed 800 Rs. as wages for 5 days for the work they did together. The man's efficiency is in work was three times that of a boy what are the daily wages of the boy?

Sol. A man and a boy received 800 Rs for 5 days.

Per day wages of the man and boy = 800/5 = 160 Rs.

The ratio of work efficiency of man and boy respectively = 3:1

Now,

3+1 = 4

4 = 160

1= 40

Hence the daily wages of the boy are 40 Rs.

Ex.5 A daily wage laborer was engaged for a certain number of days for 5750. but being absent for some of the days he was paid only Rs 5000. What was his maximum possible daily wage?

Sol. For a solution, we need to find HCF  of 5750 and 500 which is 250 Rs. Ans

For the method to find HCF Click here.

Ex.6 If 5 men or 7 women earn 5250 per day, how much 7 men and 13 women earn per day?

Sol. As given 5 men or 7 women are earning the same amount per day

5 men = 7 women

1 men = 7/5 women

7men = (7*7)/5 women = 49/5 women

7men + 13 women = 49/5 + 13 = 114/5 women

Now,

7 women = 5250 Rs. per day

1 woman = 5250/7 Rs. per day

114/5 women = (5250/7) * (114/5) = 17100Rs. Ans

This can be done by equating the total number of men.

Ex.7 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 600 rs/day how much should a woman get per day?

Sol. We are going to use Man-Day for equations.

2 men and 1 woman can do work in 14 days.

Multiply equation by 14

(2 men + 1 women)14 = 28 men + 14 women

4 women and 2 men together can do it in 8 days.

Multiply equation by 8

(4 women + 2 men)8 = 32 women + 16 men

These equations are equal because Man-Day is constant

28 men + 14 women = 32 women + 16 men

12 men = 18 women

men/women = 3/2

men : women = 3:2

A man gets 600 Rs.thus

3 = 600 

1 = 200

women has ratio 2 = 400 Rs. Ans

Ex.8 If there is a reduction in the number of workers in a factory in a ratio of 15:11 and an increment in their wages in the ratio of 20:25. then the ratio by which the total wages of the worker should be decreased is.

Sol. The ratio of total wages

15*22 : 11*25 = 6:5 Ans.

Ex.9 A sum of money is sufficient to pay A's wage for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both.

Sol. A can-do work in 21 days

B can do work in 28 days

Total work is the LCM of 21 and 28  = 84

One day work

A = 84/21 = 4

B = 84/28 = 3

A+B = 7

Together they complete work in 84/7 = 12 days.

12 days is the answer.

Ex.10 A, B, and C together earn 150 Rs/day, while A and C together earn 94 Rs. and B and  C together earn 76 Rs. the daily earning of C is?

Sol. The daily earning of c = daily earning (A+C) and (B+C) - daily earning of (A+B+C) 

= 94+76-150 = 20 Rs. Ans.

Ex.11 A skilled, a half skilled, and an unskilled laborer work for 7,8 and 10 days respectively and they together get 369 Rs. for their work. If the ratio of their everyday work is 1/3: 1/4: 1/6 then how much does the trained laborer get in Rs?

Sol. First of all, we need to simplify the ratio

1/3: 1/4: 1/6

LCM of 3,4 and 6 is 12. Multiply the ratios by 12 we get

= 4:3:2

Now calculate the man-day  ratio

4*7 : 3*8 : 2*10 =  28:24:20 

Skilled : half skilled : unskilled = 28 : 24 : 20

wages of skilled labourer  = (28/72) * 369 = 143.50 Rs. Ans

Ex.12 if a man earns 200 Rs. for his first 50 hours of work at work and is then paid one and a half times his regular hourly rate for any additional hours, then the hours must hee work to make 2300 in a week.

Sol. Rupees per hour  = 2000/50 = 40 Rs.

Now after 50 hours he will be paid 3/2 times of his wages = 40 * (3/2)  Rs per hour

After 50 hours he gets 300 Rs. let he worked for x hours

40 * (3/2) * x = 300 Rs.

x = 5 hours ans.