Test: Work & Wages - 1 - UPSC MCQ

Raman can do 1/5, Jatin can do 1/7 and Sachin can do 1/9 of the work in 1 dayRatio of their work in 1 day = 1/5 : 1/7 : 1/9
⇒ Ratio is 63 : 45 : 35 And the amount paid to them also will be in the same ratio.
⇒ Raman’s share {(63)/(63 + 45 + 35)} × 2860
∴ Raman’s share is Rs. 1260

GIVEN:
Time taken by A to complete the work = 5 days
Time taken by B to complete the work = 8 days

CONCEPT:
Here we need to find what part of money will be given to A by using unitary method of calculation.

CALCULATION:
Time taken by A to complete the work = 5 days
⇒ Work done by A in 1 day = 1/5 units
Time taken by B to complete the work = 8 days
⇒ Work done by B in 1 day = 1/8 units
Ratio of work = A : B = (1/5) : (1/8) = 8 : 5
A’s share = (8/13) × 6760
⇒ A’s share = Rs. 4160
∴ Share of A is Rs. 4160

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

As we know, Total work = Total work, so
M₁ × D₁ = M₂ × D₂ + M₃ × D₃
Given, M₁ = 105 students, D₁ = 22 days, M₂ = 105 students, D₂ = 5 days, M₃ = (105 + 14 = 119) students and D₃ = ?
M₁ × D₁ = M₂ × D₂ + M₃ × D₃
105 × 22 = 105 × 5 + 119 × D₃
2310 = 525 + 119 × D₃
119 × D₃ = 2310 – 525
D₃ = 1785/119 = 15 days

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 × (50/200) men
⇒ 30 men
∴ 30men will be catered-to with remaining meal.

Given:
A and C can do that work in 10 days.
B and C can do that work in 8 days.
The ratio of efficiencies B and C is 9:1.
The total wages for that work is 34000 Rs.

Formula Used:
Efficiency = Total work/Time taken

Calculation:
Let's assume total work = 40 Units (LCM of 8 & 10)
Efficiency of A and C = 40/10 = 4
Efficiency of B and C = 40/8 = 5
So,
Efficiency of B = 5/10 × 9 = 4.5
Efficiency of C = 5/10 × 1 = 0.5
∴ The efficiency of A = 4 - 0.5 = 3.5
Now 40 / (3.5 + 4.5) = X = 5
Value of X = 5
Wages will be divided in the ratio of efficiency so
Amount paid to A = 34000/(4.5 + 0.5 + 3.5) × 3.5 
⇒ 14000 Rs
Amount paid to B = 34000/(4.5 + 0.5 + 3.5) × 4.5
⇒ 18000 Rs
Required difference = 18000 - 14000
⇒ 4000 Rs.

Given:
P can do a piece of work = 30 days
Q can do a piece of work = 15 days
Contracted to complete the work = Rs. 60,000

Concept used:
Total work = LCM
Divide money according to the ratio of efficiency

Formula used:
Efficiency = Work/Time

Calculations:
Total work = LCM = 30

Ratio of efficiency = P ∶ Q = 1 ∶ 2
P’s share = (60,000/3) × 1 = 20,000
∴ P’s share is Rs. 20,000

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: 6 burners are used for 6 hours for 8 days with an operating cost 450 Rs.
Concept used: 

Where M₁ denotes the number of burners here.
D₁ denotes the number of Days and H1 the number of hours.
W₁ denotes the work in terms of rupees.
Calculation:
We have,

⇒ x = 16
∴ The number of burners = 16.

Given:
Let the Workers be x
X workers can finish the work = 30 days
Workers started the work = (x-10)
Total days to finish the work =  50 days

Formula:
M₁ × D₁ = M₂ ×  D₂
M₁ = Numbers of Workers Agreed for work
D₁ = Number of days Agreed for work
M₂ = Total Workers actually done the Work
D₂ = Number of days they actually finished the work

Calculation:
 M₁× D₁ = M₂ × D₂
⇒ x × 30 = (x - 10) × 50
⇒ 30x = 50x - 500
⇒ 20x = 500
⇒ x = 25
∴ Total Number of Workers Actually Agreed to Work is 25