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

Introduction

Work Rate

If a person completes a work in T days:

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

Core Relations

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

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

Work is usually assumed to be 1 unit (full work).

Combined Work Rate

If A finishes in a days, B in b days:

$$\text{Rate}_{A+B} = \frac{1}{a} + \frac{1}{b}$$

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Time together:

$$T = \frac{ab}{a+b}$$

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For three workers:

$$\text{Rate}_{A+B+C} = \frac{1}{a} + \frac{1}{b} + \frac{1}{c}$$

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LCM Method

Set Total Work = LCM of given time values, then convert time → rate.

Example:
A = 12 days
B = 8 days
Take Work = 24 units
A = 2 units/day
B = 3 units/day
Together = 5 units/day
Time =

$24/5$

Efficiency Concept

Efficiency ∝ Rate
If A is x% more efficient than B:

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

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Time ratio:

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

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Example:
A is 50% more efficient ⇒ EA : EB = 3 : 2
So TA : TB = 2 : 3

Partial Work Formula

If A works for t days:

$$\text{Work done} = t \times \frac{1}{a}$$

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Remaining work = 1 – that amount.

Then use another worker’s rate.

Alternate Days Work

If A works on Day 1, B on Day 2:

1 cycle work:

$$W_{\text{2 days}} = \frac{1}{a} + \frac{1}{b}$$

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Total time = number of full cycles + last one-person day.

Work Difference Concepts

If A alone takes a days, B takes b days, difference in one-day work:

$$\Delta = \frac{1}{a} – \frac{1}{b}$$

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Man–Day (Man–Hour) Concept

$$\text{Work} = \text{Men} \times \text{Days} \times \text{Efficiency}$$

If work remains constant:

$$M_1 D_1 E_1 = M_2 D_2 E_2$$

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Used for:

• • men joining

  • men leaving

  • work scheduling problems

Work Completion Time After Workforce Change

If x men leave:

Remaining work = Completed work removed
New time =

$$\frac{\text{Remaining Work}}{(M-x)E}$$

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Required Workers

If T days left and work pending = W units:

Required workers:

$$M = \frac{W}{D \times E}$$

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Negative Work (Reverse Worker / Damaging Worker)

If C spoils work:

$$\text{Net Rate} = R_A + R_B – R_C$$

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If C spoils faster than A and B work, work never completes.

Percentage Change in Efficiency

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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Ratio-Based Problems

If A : B efficiency = p : q
Then time ratio:

$$T_A : T_B = q : p$$

If total work = W
A’s units = p
B’s units = q

Total time together =

$$\frac{W}{p+q}$$

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Work Done in Fractions

If someone does α part of work:

Time taken =

$$T = a \times \alpha$$

If remaining fraction is β:

Remaining time =

$$T = a \times \beta$$

Short Tricks

Trick 1: Half time relation

If time decreases by 50% → efficiency doubles.

Trick 2: Work finished earlier

If work finishes k days early:

$$\text{Extra work capacity} = \frac{k}{\text{Total Time}}$$

Trick 3: A is twice as good as B

A = 2 units/day, B = 1 unit/day.

Trick 4: Multiple workers with ratio efficiencies

For efficiency ratio a:b:c, total work for time T is:

$$T(a + b + c)$$

Classic Problem Patterns

Type 1: Combined work

A+B, A+B+C etc.

Type 2: Partial work + joining

A works alone for some days, others join.

Type 3: Leave problem

Some workers leave mid-way.

Type 4: Efficiency ratio

Convert ratio → rate.

Type 5: Wages distribution

Wage ∝ work done.

Type 6: Man–day changes

Used in contractor type problems.

Type 7: Negative work

A & B work, C damages.

Type 8: Reverse calculation

Given work done fraction → find total time.

LCM-Based Templates

Template 1: A = a days, B = b days

Total = LCM(a, b)

Template 2: A = 12, B = 18

LCM = 36 units
A = 3 units/day
B = 2 units/day
Together = 5 units/day

Template 3: A = 24, B = 16, C = 12

Rates = 1, 1.5, 2 units/day (LCM = 24)
Combined = 4.5 units/day

Fastest Approach

Choose method based on problem type:

When Work Never Finishes

If damaging worker’s rate ≥ sum of good workers’ rate →
Work cannot be completed.

Practice Questions

1. A can finish a work in 12 days, B in 18 days. They work together for 4 days; remaining work done by B. Total time = ?
A) 8 days
B) 9 days
C) 10 days
D) 11 days

2. A does 40% of work in 4 days. B does 30% in 5 days. Remaining work together = ?
A) 3
B) 4
C) 5
D) 6

3. A is 60% as efficient as B. A & B together finish in 15 days. B alone = ?
A) 20
B) 22
C) 24
D) 25

4. A can do work in 10 days; B is 50% more efficient. Together = ?
A) 4
B) 5
C) 6
D) 7

5. A is 3 times as efficient as B and takes 20 days less than B. A alone = ?
A) 10
B) 12
C) 15
D) 20