Work and Wages – MBA CUET PG – Notes & Practice Questions

Fundamental Concept

If a person completes a work in T days:

$$\text{Work Rate} = \frac{1}{T} \quad (\text{work per day})$$

If rate is known:

$$\text{Time} = \frac{1}{\text{Rate}}$$

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If time is proportional to rate:

$$\text{Work} = \text{Rate} \times \text{Time}$$

Work Proportionality Rules

Rule 1: Time ∝ 1/Rate

If speed/efficiency increases, time decreases.

$$\frac{T_1}{T_2} = \frac{E_2}{E_1}$$

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Rule 2: Work is constant

If multiple workers work on the same task:

$$E_1 \times T_1 = E_2 \times T_2$$

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Combined Work

If A completes work in a days and B in b days:

$$\text{Combined Rate} = \frac{1}{a} + \frac{1}{b}$$

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$$\text{Time Together} = \frac{ab}{a + b}$$

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For 3 persons (A,B,C):

$$\text{Rate} = \frac{1}{a} + \frac{1}{b} + \frac{1}{c}$$

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LCM Method

Assign total work = LCM of time values.
Convert each worker into “work units per day.”

Example:
A = 12 days → rate = 1/12 → assume work = 60 → rate = 5 units/day.

This simplifies complex sums.

Alternate Day Work

A works 1st day, B 2nd day, repeat:

Compute:

• Combined 2-day work cycle

• Remaining work if any

Efficiency Percentage Problems

If A is x% more efficient than B:

$$\frac{E_A}{E_B} = 1 + \frac{x}{100}$$

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$$\frac{T_A}{T_B} = \frac{E_B}{E_A}$$

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Example:
A is 25% more efficient → ratio of efficiency = (5 : 4)
Time ratio = (4 : 5)

Partial Work

If a person works for t days:

$$\text{Work Done} = \text{Rate} \times t$$

Remaining work = total – completed.

Inverse Wages Concept

Wages ∝ Work Done
Wages ∝ Efficiency
Wages ∝ Time if working at constant rate

If total wage = W:

If A & B do work in ratio:

$$\frac{W_A}{W_B} = \frac{\text{Work}_A}{\text{Work}_B}$$

Group Wages Distribution

If A, B, C work together:

Wage share:

$$W_A = W \times \frac{E_A}{E_A + E_B + E_C}$$

or using time:

$$\text{Work}_A = T \times E_A$$

and then distribute proportionally.

Man–Day Concept

Work = Men × Days × Efficiency

$$W = M \times D \times E$$

If total work is constant:

$$M_1 D_1 E_1 = M_2 D_2 E_2$$

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Used for:

• Worker substitutions

• Extra men required

• Workers leaving early

Work Increase/Decrease Scenarios

If efficiency increases by x%:

$$\text{New Time} = \frac{\text{Old Time}}{1 + x/100}$$

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If efficiency decreases by x%:

$$\text{New Time} = \frac{\text{Old Time}}{1 – x/100}$$

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Pipes & Tanks (Same Logic, Applied to Work)

Filling time follows same rule:

• Rates add

• Opposite effects subtract

$$\text{Net Rate} = R_1 + R_2 – R_3$$

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Important Problem Types

Type 1: A, B, C together

Use sum of rates.

Type 2: A works alone for few days

Subtract from total work, remainder done by others.

Type 3: Worker efficiency ratios

Convert into rate ratios.

Type 4: Wages distribution

Share = proportional to work done.

Type 5: Extra workers added

Solve with:

$$M_1D_1 = M_2D_2$$

Short Tricks (High-Yield)

Trick 1: Time ratio from efficiency

If A is 50% as efficient as B:

$$E_A : E_B = 1 : 2$$

$$T_A : T_B = 2 : 1$$

Trick 2: One-third work

If full work = W and person works x days:

$$\text{fraction} = \frac{x}{\text{time to finish}}$$

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Trick 3: Joint work percentages

If A does p% and B does q% of work daily:

$$\text{Time} = \frac{100}{p+q}$$

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Trick 4: Leave day problems

If B leaves early, calculate partial work.

Trick 5: Equal work share

If 4 men finish in 12 days → total man-days = 48
If 6 men: time = 48/6 = 8 days.

Wage Distribution Examples

Given total wage W:

If A works 10 days & B works 15 days and are equally efficient:

$$W_A : W_B = 10 : 15 = 2 : 3$$

If efficiencies differ:

$$W_A : W_B = (D_A E_A) : (D_B E_B)$$

Wages Based on Work Percentage

If A completes 40% and B completes 60%:

$$W_A : W_B = 40 : 60 = 2 : 3$$

If total wage = W:

$$W_A = \frac{2W}{5}$$

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Work Rate Conversion through LCM

Example:
A = 12 days, B = 8 days → LCM = 24 units
A = 2 units/day
B = 3 units/day

Together = 5 units/day
Time = 24/5

Completion with Reduced Workforce

If x men leave, remaining men complete in t days:

$$(M-x)t = \text{Remaining Work}$$

Negative Work (Reverse Work)

Similar to pipes outlet concept:

• If worker destroys work (faulty worker)

$$\text{Net Rate} = E_1 + E_2 – E_3$$

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Common Patterns

Expect:

• Work done ratio from days or efficiency

• Incomplete work + new workers join

• Worker replaced mid-work

• Wage distribution based on time or rate

• Ratio-based efficiency problems

• Work finished earlier/later than scheduled

• Combined multiple groups

Practice Questions

1. A alone can do a work in 12 days, B alone in 18 days. They work together for 4 days and then A leaves. Remaining work finished by B in:
A) 6 days
B) 8 days
C) 9 days
D) 10 days

2. A does 30% of work in 6 days. B does 20% in 4 days. Together they finish the remaining work in:
A) 6 days
B) 7 days
C) 8 days
D) 9 days

3. A is 50% as efficient as B. Together they finish a work in 12 days. B alone would take:
A) 24
B) 30
C) 36
D) 40

4. A & B together do work in 15 days. A is 50% more efficient than B. A alone does it in:
A) 24
B) 25
C) 30
D) 36

5. A can do a job in 10 days. B is 25% more efficient. Together time = ?
A) 5
B) 6
C) 7
D) 8