Work and Wages MCQ Quiz - Objective Question with Answer for Work and Wages - Download Free PDF

Calculation

For option 3),

P, Q and R can complete a work in 24, 30 and 40 days respectively.

So, total work = LCM of 24, 30 and 40 = 120 unit

So, Efficiency of P, Q and R is 5, 4 and 3 respectively.

[Efficiency = total work / total number of days]

P works for 4 days alone.

So, P did 4 × 5 = 20 unit of work.

Q did 4 × 4 = 16 unit of work

Rest work 120 - 20 – 16 = 84

They together complete the work in  84 / [ 5 + 4 +3] = 7

Wage for per unit work is 3480 / 120 = 29

 P did = 20 + 7 × 5 = 55 unit of work.

R did 7 × 3 = 21 unit of work

So, difference between wage P and R is [ 55 – 21] × 29 = 986

So, Option 3) is satisfy. 

Given:

Money earned for 6 hours of work = ₹324

Number of hours worked = 29 hours

Formula Used:

Money earned is directly proportional to the number of hours worked.

M = k × H

where M is the money earned, H is the number of hours, and k is the proportionality constant.

Calculation:

First, find the proportionality constant k :

k = M/H

⇒ k = 324/6

⇒ k = 54

Now, calculate the money earned for 29 hours of work:

M = k × H

⇒ M = 54 × 29

⇒ M = 1,566

The amount of money earned in 29 hours is ₹1,566.

Given:

Ram alone can do the work in = 20 days

Ram and Shyam together can do the work in = 15 days

Total payment for the work = Rs.400

Formula used:

Efficiency = Total work / Days 

Shyam’s share = (Shyam's efficiency / Total efficiency) × Total payment

Calculations:

Total work (LCM of 20, 15) = 60 units

Efficiency of Ram = 60 / 20 = 3 units/day

Efficiency of (Ram + Shyam) = 60 / 15 = 4 units/day

Efficiency of Shyam = Efficiency of (Ram + Shyam) - Efficiency of Ram

Efficiency of Shyam = 4 - 3 = 1 unit/day

Share of payment is divided based on efficiency:

Total efficiency = 4 units/day

Shyam’s share = (Shyam's efficiency / Total efficiency) × Total payment

Shyam’s share = (1 / 4) × 400 = Rs.100

Shyam's share is Rs.100.

Given:

Total days = 10 days

Total payment = Rs. 10,000

Man is 50% more efficient than boy.

Formula used:

Efficiency ratio = Work ratio = Wage ratio

Calculations:

Efficiency ratio (Man : Boy) = 150 : 100 = 3 : 2

Work ratio (Man : Boy) = 3 : 2

Wage ratio (Man : Boy) = 3 : 2

Total ratio = 3 + 2 = 5

Total daily wage = 10000 / 10 = 1000

Man's daily wage ratio = 3/5

Boy's daily wage ratio = 2/5

Man's daily wage = (3/5) × 1000 = Rs. 600

Boy's daily wage = (2/5) × 1000 = Rs. 400

Difference = 600 - 400 = Rs. 200

∴ The difference between the daily wages of the man and the boy is Rs. 200.

CONCEPT:

Work and Time

• The amount of work done is inversely proportional to the number of days when the amount of work is constant.
• If two or more persons work together, their combined work per day is the sum of their individual work rates.

EXPLANATION:

• First, let's find out the work rates of Sonu and Monu:
  • Sonu can complete the work in 6 days, so his work rate is 1/6 of the work per day.
  • Monu can complete the work in 8 days, so his work rate is 1/8 of the work per day.
• When Sonu, Monu, and Ramu work together, they complete the work in 3 days. Let's denote Ramu's work rate as R (work per day).
  • The combined work rate of Sonu, Monu, and Ramu is (1/6) + (1/8) + R.
  • The total work is completed in 3 days, so their combined work rate is 1/3 of the work per day.
• (1/6) + (1/8) + R = 1/3
• (4/24) + (3/24) + R = (8/24)
  • (7/24) + R = (8/24)
  • R = (8/24) - (7/24)
  • R = 1/24
• Ramu's work rate is 1/24 of the work per day. Therefore, in 3 days, Ramu does 3 * (1/24) = 1/8 of the total work.
• The total payment for the work is ₹3600. Therefore, Ramu's share of the payment is (1/8) * 3600 = ₹450.

Therefore, the share of Ramu (in ₹) will be ₹450.

Given:

Difference between wages of A and C = Rs. 7600

Formula Used:

Share in wages = Work done/Total work × Total wages

Calculation:

Let total work be 60 unit,

Work done by A and B = 13/15 × 60 = 52 unit

⇒ Work done by C = 60 – 52 = 8 unit

Work done by B and C = 11/20 × 60 = 33 unit

⇒ Work done by A = 60 – 33 = 27 unit

Work done by B = 60 – 27 – 8 = 25 unit

According to the question,

27 – 8 = 19 unit = 7600

⇒ 1 unit = 400

Total wages of A and C = (27 + 8) = 35 units = 35 × 400 = Rs. 14000

Given:

In a camp there is a meal for 120 men or 200 children.

Calculation:

According to the question, 150 children have taken the meal

So, 50 children left

⇒ 200 children = 120 men

⇒ 50 = 120 × (\(\frac{50}{200}\)) men

⇒ 30 men

∴ 30men will be catered-to with remaining meal.

Given:

5 women and 9 girls can earn Rs.18,720 in 9 days

9 women and 16 girls earn a total of ₹ 52,080 in 14 days

Concept:

Total work = number of workers doing work × time taken to complete the work.

Calculation:

(5W + 9G) × 9 = 18,720

⇒ (5W + 9G) = 2080 ----(i)

(9W + 16G) × 14 = 52080

⇒ (9W + 16G) = 3720 ----(ii)

solving equations (i) and (ii)

⇒ 45W + 81G = 18720 ---- (iii)

⇒ 45W + 80G = 18600 ---- (iv)

by subtraction equations (iii) and (iv)

⇒ 1G = Rs. 120 

Putting the value of G in equation (i)

⇒ 5W + 1080 = 2080

⇒ 5W = 1000

⇒ W = Rs.200

According to the question:

Money earned by 12 women and 7 girls in 13days

⇒ (12 × 200 + 7 × 120) × 13

⇒ (2400 + 840) × 13

⇒ 3240 × 13 = 42120

∴ The required value is 42120.

Formula Used:

Expenditure = number of employee × average wage

Calculation:

Let the number of employee of the firm be 12x and 5x pre and post reduction respectively.

and average salary be 9y and 17 y pre and post reduction respectively.

Expenditure before reduction is 12x × 9y

Expenditure after reduction is 5x × 17y

ATQ: 12x × 9y - 5x × 17y = 46000

⇒ (108 - 85)xy = 46000

⇒ 23xy = 46000

⇒ xy = 2000

Expenditure before reduction is 12x × 9y = 108 × xy = 108 × 2000 = 216000

Expenditure before reduction is Rs. 216000.

Given:

4 men and 6 women get Rs. 1600/- by doing a piece of work in 5 days

3 men and 7 women get Rs. 1740/- by doing the same work in 6 days

 7 men and 6 women can complete the same work getting Rs. 3760/-

Calculation:

Let,

M as the rate at which one man can complete the work (in Rs./day)

W as the rate at which one woman can complete the work (in Rs./day)

From the given problem, we have two equations:

4M + 6W = 1600/5          ------- (equation 1)

3M + 7W = 1740/6          ------- (equation 2)

First, multiply equation (1) by 3 and equation (2) by 4:

12M + 18W = 960           ------- (equation 3)

12M + 28W = 1160         ------- (equation 4)

Equation (4) - Equation (3)

10W = 200

⇒ W = 200 / 10 = Rs. 20/day

Substitute W into equation (1):

4M + 6 × 20 = 320

⇒ M = 200 / 4 = Rs. 50/day

Now,

Work = Rate ×  Time

3760 = (7M + 6W) × Time

3760 = (7 × 50 + 6 × 20) × Time

3760 = (350 + 120) × Time

3760 = 470 × Time

Time = 3760 / 470 = 8 days

∴ Required number of days = 3760/470 = 8 days.

Shortcut Trick
Calculation:

⇒ \((M_1 ~+~W_1)× D_1\over (Income)_1\) = \((M_2 ~+ ~W_2) D_2\over (Income)_2\)

⇒ \((4m +6w)× 5\over 1600\) = \((3m + 7w)× 6\over 1740\)

⇒ \(4m +6w\over 3m + 7w\) = \(1600×6\over 1740×5 \)

⇒ 20 m = 50 w

⇒ m : w = 5 : 2  

Now, put the respective ratio in the equation:

⇒ \((4m +6w)× 5\over 1600\) = [(4 × 5 + 6 × 2) × 5]/1600 = 1/10 

According to the question:

⇒ \((7m + 6w)× 6\over 1740\) = [(7 × 5 + 6 × 2)× d]/3760 

⇒ 1/10 = d/80

Required number of days = 80/10 = 8 days

∴ The correct answer is 8 days.

GIVEN:

Time taken by 15 people to dig the pond = 20 days

FORMULA USED:

Man – day formula

(m₁ × d₁ × h₁)/w₁ = (m₂ × d₂ × h₂)/w₂

Where m₁, m₂ is number of persons working

d₁, d₂ is number of days taken

h_1, h₂ is number of hours

w₁, w₂ is the units of work done

CALCULATION:

15 persons have taken a job of digging a pond in 20 days

Total work = 15 × 20 = 300 units

Work done by 15 men in 10 days = 15 × 10 = 150 units

Now,

5 men left the work

Work done by 10 men in 5 days = 10 × 5 = 50 units

Again 5 men left the work

Remaining work = 300 – (150 + 50) = 100 units

⇒ Remaining work will be done in 100/5 = 20 days

∴ Total number of days taken to complete the work = 10 + 5 + 20 = 35 days

Given:-

A can do a work in 10 days

B can do a work in 12 days

they undertake to do job for Rs. 6000

Concept used:-

Efficiancy concept related to work and time.

Total work = LCM(Time taken by all individual)

Calculation:-

Total work = LCM(10, 12)

Total work = 60 units

Rs. per unit = 6000/60 = 100 Rs. per unit

∴ A's per day work = 60/10 = 6 units

A's per day income = 6 × 100 = Rs. 600

B's per day work = 60/12 = 5 units

B's per day income = 5 × 100 = Rs. 500

Let C's per day work = x units

According to Question-

⇒ (6 × 4) + (5 × 4) + (x × 4) = 60

⇒ 24 + 20 + 4x = 60

⇒ 4x = 60 - 44

⇒ x = 16/4

⇒ x = 4 units

C's per day income = 4 × 100 = Rs. 400 

∴ C should be paid for work = 400 × 4 = Rs.1600

Given:

Time is taken by A to do the work = 20 days

Time is taken by B to do the work = 30 days

Total wage = Rs. 560

Formula used:

Time = Total work/Efficiency

Concept used:

Wage is divided the same as efficiency and inversely proportional to the time taken

Calculation:

Work done by A in 1 day is = 1/20

Work done by B in 1 day is = 1/30

Work done by A and B together in 1 day is = (1/20 + 1/30) = 1/12

Work is done by A and B together in 10 days is = 10/12

Remaining work = 1 – 10/12 = 2/12 = 1/6

C do 1/6 of the work in 5 days

Total work done by C alone in 5 × 6 is = 30 days

Wages ratio of A, B and C = 1/20 × 10 : 1/30 × 10 : 1/30 × 5 = 6 : 4 : 2

Money A will get = 6/12 × 560 = 280

∴ Share of money A will get is Rs 280

 Shortcut Trick

Since A can do that piece of work in 20 days and has worked for 10 days

i.e. A has done half of total work.

So A will get half of the amount paid to all i.e. = 560/2 = Rs. 280

Confusion Points

You may think that 240 is the correct answer but it is not.

It is so because the time for which C has worked is 5 days whereas A and B have worked for 10 days. 

Thus, Wages ratio of A, B and C = 1/20 × 10 : 1/30 × 10 : 1/30 × 5 = 6 : 4 : 2

Given:-

15 boys for 5 days = at Rs 750

Calculation:-

Let 25 boys earn Rs. x in 6 days,

then according to question,

⇒ (15 × 5)/750 = (25 × 6)/x

⇒ x = 150 × 10

⇒ x = 1500

Given:

Samir's 1 day's work = 1/10

Puneet's 1 day's work = 1/15

Calculation:

(Samir + Puneet)'s 1 day's work = 1/10 + 1/15 = 1/6

(Samir + Puneet)'s 3 days work = 3 × 1/6 = 1/2

Remaining work after 3 days = 1 - 1/2 = 1/2

Remaining work completed in 2 days.

(Samir + Puneet + Ashok)'s 1 day's work = 1/2 × 1/2 = 1/4

Ashok's 1 day's work = 1/4 - 1/6 = 1/12

Ratio of work done = 5/10 : 5/15 : 2/12

= 1/2 : 1/3 : 1/6

= 3 : 2 : 1

∴ Ashok's share = 1/6 × 4500 = Rs.750

Alternate Method Samir and Puneet can complete the same work in 10 days and 15 days respectively

Total work = LCM(10, 15) = 30 units 

Efficiency of Samir = 30/10 = 3 units

Efficiency of Puneet = 30/15 = 2 units 

According to the question,

Samir and Puneet worked for (3 + 2) = 5 days 

Work done by Samir and Puneet in 5 days = 5 × 5 = 25 units 

Remaining 5 units of work is done by Ashok in 2 days

Efficiency of Ashok = 5/2 = 2.5 units 

Total amount = Rs. 4500

Amount given for 1 unit of work = 4500/30 = 150

Amount given to Ashok = 150 × 5 = Rs. 750