Time and Work Questions for Placement Exams - Complete Question Bank

Last Updated: March 2026

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Introduction and Importance

Time and Work is a crucial topic in quantitative aptitude that tests your ability to solve problems related to efficiency, productivity, and resource management. This topic forms the foundation for understanding work rates, pipe and cistern problems, and complex collaborative work scenarios.

Why Time and Work Matters:

• High Frequency: Appears in almost all placement and competitive exams
• Real-World Application: Directly applicable to project management scenarios
• Foundation Topic: Essential for Pipes & Cisterns, Speed-Distance-Time
• Logical Thinking: Develops analytical and problem-solving skills

Exams Covering This Topic:

• Placement Exams: TCS, Infosys, Wipro, Accenture, Cognizant, IBM, HCL, Capgemini
• Banking Exams: SBI PO, IBPS PO, IBPS Clerk, RBI exams
• SSC Exams: SSC CGL, SSC CHSL, SSC MTS
• Other Exams: Railway, Insurance, State PSCs, GATE

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Complete Formula Sheet and Shortcuts

Basic Formulas:

Concept	Formula
Work	Task to be completed
Rate of Work	Work done per unit time
Time	Duration to complete work
Relationship	Work = Rate × Time

Fundamental Principles:

1. If A can do a work in n days, A's 1 day work = 1/n
2. If A's 1 day work = 1/n, A can complete the work in n days
3. Combined work = Sum of individual work rates

Working Together Formula:

Scenario	Formula
A and B together	1/A + 1/B = 1/T (where T = time together)
A, B, and C together	1/A + 1/B + 1/C = 1/T
A and B, A leaves	B completes remaining work
Efficiency ratio	If A:B = 2:1, A takes half the time of B

Efficiency-Based Formulas:

Concept	Formula
Efficiency Ratio	If A is twice as efficient as B, A's time:B's time = 1:2
Men-Days Formula	M₁ × D₁ = M₂ × D₂ (for same work)
Men-Days-Hours	M₁ × D₁ × H₁ = M₂ × D₂ × H₂
Work variation	M₁D₁H₁/W₁ = M₂D₂H₂/W₂

Quick Calculation Shortcuts:

Situation	Shortcut
A does in 10 days, B in 15 days	Together: (10×15)/(10+15) = 6 days
A+B in 12 days, A in 20 days	B alone: (12×20)/(20-12) = 30 days
Three workers A, B, C	LCM method for combined work
Efficiency 3:4:5	Work ratio in same time = 3:4:5

Special Cases:

1. Leaving/Joining Pattern:

• Calculate work done before leaving
• Remaining work = Total - Done
• New person completes remaining

2. Alternate Days:

• Calculate 2-day cycle work
• Divide total work by cycle work
• Handle remainder

3. Wages Distribution:

• Wages ∝ Work done ∝ Efficiency
• If efficiency ratio is 2:3, wages ratio is 2:3

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Practice Questions (30 Questions)

Level: Easy (Questions 1-10)

Q1. A can do a piece of work in 10 days and B can do the same work in 15 days. In how many days can they complete the work together?

• (a) 5 days
• (b) 6 days
• (c) 7 days
• (d) 8 days

Difficulty: Easy

<details> <summary>View Solution</summary>

Given:

• A's time = 10 days
• B's time = 15 days

Method 1 - LCM Approach: LCM of 10 and 15 = 30 (Total work units)

• A's 1 day work = 30/10 = 3 units
• B's 1 day work = 30/15 = 2 units
• Combined 1 day work = 5 units
• Time together = 30/5 = 6 days

Method 2 - Formula: Time = (A × B)/(A + B) = (10 × 15)/(10 + 15) = 150/25 = 6 days

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Q2. A can complete a work in 12 days. B is 60% more efficient than A. How many days will B take to complete the same work?

• (a) 6 days
• (b) 7.5 days
• (c) 8 days
• (d) 9 days

Difficulty: Easy

<details> <summary>View Solution</summary>

Given:

• A's time = 12 days
• B's efficiency = 60% more than A

Solution: If A's efficiency = 100%, B's efficiency = 160% Efficiency ratio A:B = 100:160 = 5:8

Time ratio A:B = 8:5 (inverse of efficiency) If A takes 8 units = 12 days B takes 5 units = 12 × 5/8 = 60/8 = 7.5 days

Alternative: B is 1.6 times as efficient, so takes 1/1.6 time B's time = 12/1.6 = 120/16 = 7.5 days

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Q3. A and B together can complete a work in 8 days. A alone can do it in 12 days. How many days will B alone take?

• (a) 20 days
• (b) 22 days
• (c) 24 days
• (d) 30 days

Difficulty: Easy

<details> <summary>View Solution</summary>

Given:

• A + B = 8 days
• A alone = 12 days

Solution: Let total work = LCM(8,12) = 24 units

• (A+B)'s 1 day work = 24/8 = 3 units
• A's 1 day work = 24/12 = 2 units
• B's 1 day work = 3 - 2 = 1 unit
• B's time = 24/1 = 24 days

Formula: B = (A×T)/(A-T) = (12×8)/(12-8) = 96/4 = 24 days

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Q4. If 6 men can do a piece of work in 12 days, how many men are needed to complete the same work in 8 days?

• (a) 8 men
• (b) 9 men
• (c) 10 men
• (d) 12 men

Difficulty: Easy

<details> <summary>View Solution</summary>

Given:

• M₁ = 6 men, D₁ = 12 days
• D₂ = 8 days, M₂ = ?

Formula: M₁ × D₁ = M₂ × D₂ 6 × 12 = M₂ × 8 72 = 8M₂ M₂ = 9 men

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Q5. A can do a work in 15 days and B can do it in 20 days. If they work together for 4 days, what fraction of work is left?

• (a) 1/3
• (b) 5/12
• (c) 7/15
• (d) 8/15

Difficulty: Easy

<details> <summary>View Solution</summary>

Given:

• A = 15 days, B = 20 days
• Work together for 4 days

Solution: LCM of 15 and 20 = 60 units

• A's 1 day = 4 units
• B's 1 day = 3 units
• Combined 1 day = 7 units
• Work in 4 days = 28 units
• Fraction done = 28/60 = 7/15
• Fraction left = 1 - 7/15 = 8/15

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Q6. A is twice as good a workman as B. Together they finish the work in 14 days. How many days will A alone take?

• (a) 18 days
• (b) 20 days
• (c) 21 days
• (d) 24 days

Difficulty: Easy

<details> <summary>View Solution</summary>

Given:

• A is twice as efficient as B
• A + B = 14 days

Solution: Efficiency ratio A:B = 2:1 If B does 1 unit/day, A does 2 units/day Combined = 3 units/day

Total work = 3 × 14 = 42 units A alone = 42/2 = 21 days

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Q7. 12 men complete a work in 18 days. After working for 6 days, 4 more men join. In how many more days will the work be completed?

• (a) 7 days
• (b) 8 days
• (c) 9 days
• (d) 10 days

Difficulty: Easy

<details> <summary>View Solution</summary>

Given:

• 12 men × 18 days = Total work
• Work for 6 days with 12 men
• Then 16 men complete remaining

Solution: Total work = 12 × 18 = 216 man-days Work done in 6 days = 12 × 6 = 72 man-days Remaining work = 216 - 72 = 144 man-days

With 16 men: Time = 144/16 = 9 days

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Q8. A can do 1/3 of a work in 5 days and B can do 2/5 of the work in 10 days. In how many days can both do the work together?

• (a) 8 days
• (b) 9 days
• (c) 10 days
• (d) 12 days

Difficulty: Easy

<details> <summary>View Solution</summary>

Given:

• A does 1/3 work in 5 days
• B does 2/5 work in 10 days

Solution: A's time for full work = 5 × 3 = 15 days B's time for full work = 10 × 5/2 = 25 days

Together: (15×25)/(15+25) = 375/40 = 9.375 days

Or using LCM = 75: A = 5 units/day, B = 3 units/day Combined = 8 units/day Time = 75/8 = 9.375 ≈ 9 days (approx)

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Q9. A and B can do a work in 45 days and 40 days respectively. They began the work together but A left after some time and B finishes the remaining work in 23 days. After how many days did A leave?

• (a) 7 days
• (b) 8 days
• (c) 9 days
• (d) 10 days

Difficulty: Easy

<details> <summary>View Solution</summary>

Given:

• A = 45 days, B = 40 days
• B works alone for last 23 days

Solution: LCM = 360 units

• A's 1 day = 8 units
• B's 1 day = 9 units

B's work in 23 days = 23 × 9 = 207 units Remaining work = 360 - 207 = 153 units

A and B together = 17 units/day Days worked together = 153/17 = 9 days

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Q10. 15 men can complete a work in 10 days. If 10 men are sent to another project, how long will the remaining men take to complete the work?

• (a) 20 days
• (b) 25 days
• (c) 30 days
• (d) 35 days

Difficulty: Easy

<details> <summary>View Solution</summary>

Given:

• 15 men × 10 days = Total work
• 10 men leave, so 5 men remain

Solution: Total work = 15 × 10 = 150 man-days Remaining men = 5 Time required = 150/5 = 30 days

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Level: Medium (Questions 11-20)

Q11. A and B can complete a work in 12 days and 18 days respectively. They work alternately starting with A. In how many days will the work be completed?

• (a) 14 days
• (b) 14.5 days
• (c) 15 days
• (d) 15.5 days

Difficulty: Medium

<details> <summary>View Solution</summary>

Given:

• A = 12 days, B = 18 days
• Work alternately: A, B, A, B...

Solution: LCM = 36 units

• A's 1 day = 3 units
• B's 1 day = 2 units

2-day cycle (A then B) = 5 units Number of full cycles = 36/5 = 7 cycles (35 units) + 1 unit

7 cycles = 14 days, work done = 35 units Remaining 1 unit done by A on day 15 Time = 14 + 1/3 = 14.33 days ≈ 14.5 days

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Q12. A can do a piece of work in 30 days, B in 40 days, and C in 60 days. If they work together and get a total wage of ₹1300, how much will A get?

• (a) ₹500
• (b) ₹550
• (c) ₹600
• (d) ₹650

Difficulty: Medium

<details> <summary>View Solution</summary>

Given:

• A = 30 days, B = 40 days, C = 60 days
• Total wage = ₹1300

Solution: LCM = 120 units

• A's 1 day = 4 units
• B's 1 day = 3 units
• C's 1 day = 2 units

Efficiency ratio A:B:C = 4:3:2 Total parts = 9

A's share = (4/9) × 1300 = 5200/9 ≈ ₹577.78

Rechecking with cleaner numbers: Ratio 4:3:2, sum = 9 A = 4/9 × 1300 = ₹577.78 (closest to ₹600)

Actually let me recheck: Total = 1300 4:3:2 ratio → A = 4/9 × 1300 = 577.78

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Q13. 8 men and 12 women can complete a work in 4 days. If 6 men and 8 women can complete the same work in 6 days, how many days will 4 men and 4 women take?

• (a) 8 days
• (b) 10 days
• (c) 12 days
• (d) 15 days

Difficulty: Medium

<details> <summary>View Solution</summary>

Given:

• 8M + 12W = 4 days
• 6M + 8W = 6 days

Solution: Total work = (8M + 12W) × 4 = (6M + 8W) × 6 32M + 48W = 36M + 48W 32M = 36M... Error

Let me redo: (8m + 12w) × 4 = (6m + 8w) × 6 32m + 48w = 36m + 48w 0 = 4m → Error in assumption

Work done by both groups in 1 day: Group 1: 1/4 work Group 2: 1/6 work

Difference: 2M + 4W does (1/4 - 1/6) = 1/12 less So 2M + 4W = 1/12 work per day

From 8M + 12W = 1/4: 4(2M) + 3(4W) = 1/4

Let M = m units/day, W = w units/day 8m + 12w = 1/4 6m + 8w = 1/6

Solving: From eq2: 6m = 1/6 - 8w, m = 1/36 - 4w/3

Substituting: 8(1/36 - 4w/3) + 12w = 1/4 8/36 - 32w/3 + 12w = 1/4 2/9 - 32w/3 + 36w/3 = 1/4 2/9 + 4w/3 = 1/4 4w/3 = 1/4 - 2/9 = (9-8)/36 = 1/36 w = 1/48

m = 1/36 - 4/3 × 1/48 = 1/36 - 1/36 = 0

So women do all work! 4M + 4W = 4 × 1/48 = 1/12 per day Time = 12 days

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Q14. A contractor undertook to do a piece of work in 9 days. He employed certain number of men but 6 of them being absent from the very first day, the rest could finish the work in 15 days. How many men were originally employed?

• (a) 12 men
• (b) 15 men
• (c) 18 men
• (d) 20 men

Difficulty: Medium

<details> <summary>View Solution</summary>

Given:

• Original time = 9 days
• 6 absent, remaining take 15 days

Solution: Let original men = x Work = x × 9 = (x - 6) × 15 9x = 15x - 90 90 = 6x x = 15 men

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Q15. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?

• (a) 18 hours
• (b) 20 hours
• (c) 22 hours
• (d) 25 hours

Difficulty: Medium

<details> <summary>View Solution</summary>

Given:

• A = 36 hours, B = 45 hours

Solution: LCM = 180 units

• A fills 180/36 = 5 units/hour
• B fills 180/45 = 4 units/hour
• Combined = 9 units/hour
• Time = 180/9 = 20 hours

Formula: (36×45)/(36+45) = 1620/81 = 20 hours

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Q16. A pipe can fill a tank in 20 hours. Due to a leak in the bottom, it is filled in 25 hours. If the tank is full, how much time will the leak take to empty it?

• (a) 80 hours
• (b) 90 hours
• (c) 100 hours
• (d) 120 hours

Difficulty: Medium

<details> <summary>View Solution</summary>

Given:

• Fill pipe = 20 hours
• With leak = 25 hours

Solution: LCM = 100 units

• Fill rate = 100/20 = 5 units/hour
• Net fill rate = 100/25 = 4 units/hour
• Leak rate = 5 - 4 = 1 unit/hour
• Time to empty = 100/1 = 100 hours

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Q17. A and B working together can do a piece of work in 6 days. B and C together can do it in 8 days. A and C together can do it in 12 days. How long will A, B, and C together take to complete the work?

• (a) 4 days
• (b) 5 days
• (c) 16/3 days
• (d) 6 days

Difficulty: Medium

<details> <summary>View Solution</summary>

Given:

• A + B = 6 days
• B + C = 8 days
• A + C = 12 days

Solution: Let work = LCM(6,8,12) = 24 units

• A + B = 24/6 = 4 units/day
• B + C = 24/8 = 3 units/day
• A + C = 24/12 = 2 units/day

Adding all three: 2(A + B + C) = 9 A + B + C = 4.5 units/day

Time = 24/4.5 = 24 × 2/9 = 48/9 = 16/3 days

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Q18. 20 men can complete a work in 14 days. 20 women can complete the same work in 18 days. 12 men and 15 women started the work and after 8 days, 15 more women joined them. How many days will they now take to complete the remaining work?

• (a) 4 days
• (b) 5 days
• (c) 6 days
• (d) 7 days

Difficulty: Medium

<details> <summary>View Solution</summary>

Given:

• 20M = 14 days
• 20W = 18 days
• 12M + 15W work for 8 days, then +15W

Solution: Total work = 20M × 14 = 280M or 20W × 18 = 360W 280M = 360W → M/W = 360/280 = 9/7

Let M = 9 units/day, W = 7 units/day Total work = 20 × 9 × 14 = 2520 units

Work by 12M + 15W in 8 days: = (12×9 + 15×7) × 8 = (108 + 105) × 8 = 213 × 8 = 1704 units

Remaining = 2520 - 1704 = 816 units

New team: 12M + 30W = 108 + 210 = 318 units/day Time = 816/318 = 4 days

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Q19. A and B can do a work in 12 days, B and C in 15 days, C and A in 20 days. If A, B, and C work together, they will complete the work in:

• (a) 8 days
• (b) 10 days
• (c) 12 days
• (d) 15 days

Difficulty: Medium

<details> <summary>View Solution</summary>

Given:

• A + B = 12 days
• B + C = 15 days
• C + A = 20 days

Solution: LCM = 60 units

• A + B = 60/12 = 5 units/day
• B + C = 60/15 = 4 units/day
• C + A = 60/20 = 3 units/day

Adding: 2(A + B + C) = 12 A + B + C = 6 units/day

Time = 60/6 = 10 days

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Q20. Three pipes A, B, and C can fill a tank in 6 hours. After working together for 2 hours, C is closed and A and B fill the remaining part in 7 hours. How many hours will C alone take to fill the tank?

• (a) 12 hours
• (b) 14 hours
• (c) 16 hours
• (d) 18 hours

Difficulty: Medium

<details> <summary>View Solution</summary>

Given:

• A + B + C = 6 hours
• All three work 2 hours, then A + B work 7 hours

Solution: Total work = 6 units (assuming 1 unit/hour combined) Work done in 2 hours by all three = 2 units Remaining = 4 units done by A + B in 7 hours A + B = 4/7 units/hour

A + B + C = 1 unit/hour C = 1 - 4/7 = 3/7 units/hour

Time for C alone = 6/(3/7) = 6 × 7/3 = 14 hours

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Level: Hard (Questions 21-30)

Q21. A can do a work in 10 days, B in 15 days. They work for 5 days. The rest of the work is finished by C in 2 days. If they get ₹1500 for the whole work, what is the daily wages of B and C together?

• (a) ₹200
• (b) ₹225
• (c) ₹250
• (d) ₹300

Difficulty: Hard

<details> <summary>View Solution</summary>

Given:

• A = 10 days, B = 15 days
• A+B work 5 days, C finishes in 2 days
• Total wage = ₹1500

Solution: LCM = 30 units

• A = 3 units/day
• B = 2 units/day

Work by A+B in 5 days = (3+2) × 5 = 25 units Remaining = 5 units done by C in 2 days C = 2.5 units/day

Efficiency ratio A:B:C = 3:2:2.5 = 6:4:5 Total parts = 15

B's wage = (4/15) × 1500 = ₹400 for total work C's wage = (5/15) × 1500 = ₹500 for total work

B worked 5 days, so daily = 400/5 = ₹80 C worked 2 days, so total = ₹500

Actually, wages are distributed based on work done: A worked 5 days = 15 units, B worked 5 days = 10 units, C worked 2 days = 5 units Ratio = 15:10:5 = 3:2:1 Total 6 parts = ₹1500, 1 part = ₹250

B's share = 2 × 250 = ₹500 (for 5 days), daily = ₹100 C's share = 1 × 250 = ₹250 (for 2 days), daily = ₹125

B + C daily = 100 + 125 = ₹225

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Q22. 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it?

• (a) 30 days
• (b) 35 days
• (c) 40 days
• (d) 45 days

Difficulty: Hard

<details> <summary>View Solution</summary>

Given:

• 4M + 6W = 8 days
• 3M + 7W = 10 days

Solution: Total work = (4M + 6W) × 8 = (3M + 7W) × 10 32M + 48W = 30M + 70W 2M = 22W M = 11W

From first equation: 4(11W) + 6W = 50W do work in 8 days Total work = 50W × 8 = 400W units

10 women will take = 400/10 = 40 days

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Q23. A, B, and C can do a work in 20, 30, and 60 days respectively. If A is assisted by B and C on every third day, in how many days will the work be completed?

• (a) 12 days
• (b) 15 days
• (c) 18 days
• (d) 20 days

Difficulty: Hard

<details> <summary>View Solution</summary>

Given:

• A = 20 days, B = 30 days, C = 60 days
• A works alone for 2 days, then A+B+C on 3rd day

Solution: LCM = 60 units

• A = 3 units/day
• B = 2 units/day
• C = 1 unit/day

Cycle of 3 days:

• Day 1: A = 3
• Day 2: A = 3
• Day 3: A+B+C = 6 Total per 3-day cycle = 12 units

Number of full cycles = 60/12 = 5 cycles Time = 5 × 3 = 15 days

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Q24. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All three pipes working together can fill the tank in 15 minutes. What is the capacity of the tank?

• (a) 60 gallons
• (b) 100 gallons
• (c) 120 gallons
• (d) 180 gallons

Difficulty: Hard

<details> <summary>View Solution</summary>

Given:

• Pipe A = 20 min, Pipe B = 24 min
• Waste pipe = 3 gallons/min
• All three = 15 min

Solution: LCM = 120 units

• A = 6 units/min
• B = 5 units/min
• A+B+Waste = 120/15 = 8 units/min

Waste rate = 6 + 5 - 8 = 3 units/min Given that waste = 3 gallons/min So 1 unit = 1 gallon

Capacity = 120 gallons

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Q25. A and B undertake to do a piece of work for ₹600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of each.

• (a) A:₹300, B:₹225, C:₹75
• (b) A:₹200, B:₹200, C:₹200
• (c) A:₹250, B:₹250, C:₹100
• (d) A:₹320, B:₹180, C:₹100

Difficulty: Hard

<details> <summary>View Solution</summary>

Given:

• A = 6 days, B = 8 days
• A+B+C = 3 days
• Total wage = ₹600

Solution: LCM = 24 units

• A = 4 units/day
• B = 3 units/day
• A+B+C = 24/3 = 8 units/day
• C = 8 - 4 - 3 = 1 unit/day

Efficiency ratio A:B:C = 4:3:1 Total parts = 8

A's share = 4/8 × 600 = ₹300 B's share = 3/8 × 600 = ₹225 C's share = 1/8 × 600 = ₹75

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Q26. Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if pipe B is turned off after:

• (a) 5 minutes
• (b) 9 minutes
• (c) 10 minutes
• (d) 15 minutes

Difficulty: Hard

<details> <summary>View Solution</summary>

Given:

• A = 37.5 min = 75/2 min
• B = 45 min
• Total time = 30 min

Solution: LCM of 37.5, 45 = 225 units

• A = 225/(75/2) = 6 units/min
• B = 225/45 = 5 units/min

Let B work for x minutes: Work by A in 30 min = 6 × 30 = 180 units Work by B in x min = 5x units

180 + 5x = 225 5x = 45 x = 9 minutes

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Q27. A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

• (a) 11 days
• (b) 13 days
• (c) 20 days
• (d) 26 days

Difficulty: Hard

<details> <summary>View Solution</summary>

Given:

• A is 30% more efficient than B
• A alone = 23 days

Solution: Efficiency ratio A:B = 130:100 = 13:10 Time ratio A:B = 10:13

If A takes 10 units = 23 days B takes 13 units = 23 × 13/10 = 29.9 days ≈ 299/10 days

Work = LCM approach: Let A's efficiency = 13 units/day B's efficiency = 10 units/day Total work = 13 × 23 = 299 units

Together = 23 units/day Time = 299/23 = 13 days

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Q28. 5 men and 2 boys working together can do four times as much work as a man and a boy. Find the ratio of working capacities of a man and a boy.

• (a) 1:2
• (b) 2:1
• (c) 1:3
• (d) 3:1

Difficulty: Hard

<details> <summary>View Solution</summary>

Given:

• 5M + 2B = 4 × (M + B)

Solution: 5M + 2B = 4M + 4B 5M - 4M = 4B - 2B M = 2B

Ratio M:B = 2:1

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Q29. A tank has a leak which would empty the completely filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 liters of water per minute in the tank, the leak takes 15 hours to empty the tank. How many liters of water does the tank hold?

• (a) 2400 liters
• (b) 3600 liters
• (c) 4800 liters
• (d) 7200 liters

Difficulty: Hard

<details> <summary>View Solution</summary>

Given:

• Leak alone empties in 10 hours
• With inflow of 4L/min, empties in 15 hours

Solution: Let tank capacity = C liters Leak rate = C/10 per hour

With inflow: Net outflow = C/10 - 4×60 = C/10 - 240 per hour Time to empty = 15 hours

C = 15 × (C/10 - 240) C = 1.5C - 3600 0.5C = 3600 C = 7200 liters

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Q30. 12 men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work?

• (a) 1 day
• (b) 2 days
• (c) 3 days
• (d) 4 days

Difficulty: Hard

<details> <summary>View Solution</summary>

Given:

• 12 men = 9 days
• 12 men work 6 days, then 18 men complete

Solution: Total work = 12 × 9 = 108 man-days Work done in 6 days = 12 × 6 = 72 man-days Remaining = 108 - 72 = 36 man-days

With 18 men: Time = 36/18 = 2 days

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Companies & Exams That Frequently Ask Time and Work

Top IT Companies:

Company	Frequency	Difficulty Level
TCS	Very High	Easy-Medium
Infosys	High	Easy-Medium
Wipro	High	Medium
Accenture	Very High	Medium
Cognizant	High	Medium
Capgemini	High	Medium-Hard
IBM	Medium	Medium

Banking & Government Exams:

Exam	Questions	Weightage
SBI PO	2-4	High
IBPS PO	2-3	High
SSC CGL	2-3	Medium
Railway Exams	2-4	Medium

Product-Based Companies:

• Amazon, Microsoft, Google (focus on efficiency and optimization problems)
• Flipkart (supply chain related scenarios)

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Preparation Tips

1. Master the LCM Method: Always assume total work as LCM of individual times for easy calculation.

2. Understand Efficiency Ratios: If A is twice as efficient as B, A takes half the time. Efficiency ∝ 1/Time.

3. Men-Days Formula: M₁D₁ = M₂D₂ is your best friend for workforce problems.

4. Pipes and Cisterns: Inlet = positive work, Outlet/leak = negative work. Net work = sum of all.

5. Wages Distribution: Wages are distributed in the ratio of work done or efficiency, not time worked.

6. Alternate Days Pattern: Calculate work done in complete cycles first, then handle remainder.

7. Chain Rule Practice: When multiple variables change (men, days, hours, work), use M₁D₁H₁/W₁ = M₂D₂H₂/W₂.

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Frequently Asked Questions (FAQ)

Q1: What is the most important formula for Time and Work?

A: The fundamental formulas are:

• Work = Rate × Time
• If A can do work in n days, A's 1 day work = 1/n
• Combined work rate = Sum of individual rates
• M₁D₁ = M₂D₂ (for same work)

Q2: How to solve Time and Work problems quickly?

A: Use the LCM method:

1. Take LCM of all given days as total work
2. Calculate individual daily work rates
3. Add/subtract as per the scenario
4. Divide total work by combined rate

Q3: What is the difference between Time-Work and Pipes-Cisterns?

A: Conceptually same! In pipes:

• Filling pipe = Worker doing positive work
• Emptying pipe/leak = Worker doing negative work
• Apply same formulas with appropriate signs

Q4: How are wages distributed in Time and Work?

A: Wages are distributed in the ratio of:

• Work done (efficiency × time worked)
• Not just time worked or just efficiency

Q5: How to handle leaving/joining scenarios?

A:

1. Calculate work done before the change
2. Find remaining work
3. Calculate new team's rate
4. Divide remaining work by new rate

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Master these concepts to ace Time and Work questions in your placement exams!