# Work and Wages

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## Basic Concept with Examples

### FORMULAS:

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)

Q1) A, B and C contract to do a work for Rs 6500. A can do the work in 10 days, B in 15 days and C in 20 days. If they work together to do the work, what is the share of B?
1) Rs 2000
2) Rs 3000
3) Rs 1500
4) Rs 2500

Solution:

Work = LCM(10, 15, 20) = 60 units
Work done in a day: A = 6 units/day, B = 4 units/day, C = 3 units/day
Share of B = (4/13) × 6500 = Rs 2000
Hence, option 1.

Q2) A can finish a work in 15 days, B in 20 days and C in 25 days. All these three worked together and earned Rs 4700. The share of C is
1) Rs 1200
2) Rs 1500
3) Rs 1800
4) Rs 2000

Solution:

Work = LCM(15, 20, 25) = 300 units
Work done in a day: A = 20 units/day, B = 15 units/day, C = 12 units/day
Share of C = (12/47) × 4700 = Rs 1200
Hence, option 1.

Q3) A and B undertake to do a piece of work for Rs 1200. A alone can do it in 8 days, while B can do it in 6 days. With the help of C, they complete it in 3 days. Find the share of C.
1) Rs 450
2) Rs 300
3) Rs 150
4) Rs 100

Solution:

Work = LCM(8, 6, 3) = 24 units
Work done in a day: A = 3 units/day, B = 4 units/day, A + B + C = 8 units/day
C = 1 unit/day
C = (1/8) × 1200 = Rs 150
Hence, option 3.

Q4) Ram can do a work in 20 days. Ram and Shyam together do the same work in 15 days. I they are paid Rs 400 for the work, what is the share of each?
1) Rs 300, Rs 100
2) Rs 200, Rs 200
3) Rs 250, Rs 150
4) Rs 350, Rs 50

Solution:

Work = LCM(15, 20) = 60 units
Work done in a day: Ram = 3 units/day
Ram + Shyam = 4 units/day i.e. Shyam = 1 unit/day
Share of Ram = (3/4) × 400 = Rs 300
Share of Shyam = (1/4) × 400 = Rs 100
Hence, option 1.

Q5) A, B and C undertake to do a piece of work for Rs 660. A and B together do 8/11 of the work and the rest is done by C alone. How much should C get?
1) Rs 160
2) Rs 200
3) Rs 190
4) Rs 180

Solution:

As A and B together do 8/11 of the work so, C does 3/11 of the work.
Share of C = (3/11) × 660 = Rs 180
Hence, option 4.

Q6) A, B and C undertake to do a piece of work for Rs 480. A and B together do 1/4 of the work and the rest is done by C alone. How much should C get?
1) Rs 360
2) Rs 120
3) Rs 240
4) Rs 180

Solution:

As A and B together do 1/4 of the work so, C does 3/4 of the work.
Share of C = (3/4) × 480 = Rs 360
Hence, option 1.

Q7) Wages of 20 boys for 15 days is Rs 9000. The daily wage of a man is 1.5 times that of a boy. How many men must work for 30 days to earn Rs 13500?
1) 12 men
2) 20 men
3) 16 men
4) 10 men

Solution:

Wages of 20 boys for 15 days is Rs 9000
Wage of 1 boy for 15 days is Rs 450
Wage of 1 boy for a day is Rs 30
Wage of a man for a day is Rs 45
Wage of a man for 30 days is Rs 1350
So, 10 men earn Rs 13500 in 30 days
Hence, option 4.

Q8) 4 men and 6 boys earn Rs 1600 in 5 days. 3 men and 7 boys earn Rs 1740 in 6 days. In how many days will 7 men and 6 boys earn Rs 3760.
1) 8 days
2) 10 days
3) 6 days
4) 12 days

Solution:

Wage of a man per day = Rs m
Wage of a boy per day = Rs b
4 men and 6 boys earn Rs 1600 in 5 days i.e. Rs 320 in a day
4m + 6b = 320 i.e. 2m + 3b = 160 – eq 1
3 men and 7 boys earn Rs 1740 in 6 days i.e. Rs 290 in a day
3m + 7b = 290 – eq 2
From equation 1, 2
b = 20, m = 50
7 men and 6 boys earn 7×50 + 6×20 = Rs 470 in a day i.e. Rs 3760 in 8 days.
Hence, option 1.

Q9) A, B and C together earn Rs 640 in 8 days. A and C together earn Rs 250 in 5 days. B and C together earn Rs 420 in 6 days. Find the daily earning of C.
1) Rs 60
2) Rs 40
3) Rs 80
4) Rs 50

Solution:

A + B + C = Rs 80/day
A + C = Rs 50/day
B + C = Rs 70/day
A + C + B + C = Rs 120/day
80 + C = 120 i.e. C = Rs 40/day
Hence, option 2.

Q10) A, B and C together earn Rs 1500 in 10 days. A and C together earn Rs 800 in 8 days. B and C together earn Rs 900 in 9 days. Find the daily earning of B.
1) Rs 60
2) Rs 50
3) Rs 30
4) Rs 40

Solution:

A + B + C = Rs 150/day
A + C = Rs 100/day
B + C = Rs 100/day
A + C + B + C = Rs 200/day
150 + C = 200 i.e. C = Rs 50/day
Hence, option 2.

Q11) A, B and C can do a piece of work in 20, 24 and 30 days, respectively. They undertook to do the piece of work for Rs 5400. They began the work together but B left 2 days before the completion of work and C left 5 days before the completion of the work. The share of A from the assured money is
1) Rs 2700
2) Rs 540
3) Rs 1800
4) Rs 600

Solution:

Work = LCM(20, 24, 30) = 120 units
Work done in a day: A = 6 units/day, B = 5 units/day, C = 4 units/day
Work is completed in 'n' days. 6n + 5(n - 2) + 4(n - 5) = 120 i.e. n = 10
Work done by A = 6n = 6×10 = 60 units Share of A = (60/120) × 5400 = Rs 2700
Hence, option 1.

Q12) 2 men and 1 woman can do a piece of work in 14 days, while 4 women and 2 men can do the same work in 8 days. If a man gets Rs 90 per day, what should be the wages per day of a women?
1) Rs 48
2) Rs 60
3) Rs 72
4) Rs 135

Solution:

Work done by a man in a day = m units
Work done by a women in a day = w units
As 2 men and 1 woman can do a piece of work in 14 days so, Work = (2m + w)×14
As 2 men and 4 women can do a piece of work in 8 days so, Work = (2m + 4w)×8
(2m + 4w)×8 = (2m + w)×14
3w = 2m
w = (2/3)m
As work done by a women in a day is 2/3 rd of the work done by a man in a day so, wage per day of a women is (2/3)×90 = Rs 60
Hence, option 2.