Time and Work Aptitude Questions with Solutions

Time and Work problems reduce to one step: express each worker’s output as a fraction of the job per day, then add the fractions. Departure problems, workforce changes, and pipes and cisterns all follow the same structure.

The Core Method: Work Rates

A worker who finishes a job in 10 days completes 1/10 of the job each day. A second worker who finishes the same job in 15 days completes 1/15 per day. Together, they finish 1/10 + 1/15 of the job each day. That sum, inverted, gives the combined time.

The LCM shortcut reduces arithmetic errors. For the 10-day and 15-day example, LCM(10, 15) = 30. Express rates as 3/30 and 2/30. Sum = 5/30. Combined time = 30 / 5 = 6 days. For three-worker problems, tracking three unequal fractions through several additions is where errors creep in; finding the LCM once at the start removes that risk.

The framing handles every T&W variant:

• Two or more workers together: add their rates, then invert.
• One worker leaves mid-job: apply the combined rate for the overlap period, then switch to the remaining worker’s rate for the rest.
• Workforce expands mid-job: recalculate using the new total at the new rate.
• Pipes and cisterns: filling pipes add rate, emptying pipes subtract it.

Four Question Types You Will See

Campus aptitude tests cluster Time and Work questions around four patterns. Identifying the type before calculating is worth 20 to 30 seconds per question.

Type 1: Combined Rate

Given each worker’s individual time, find the time for two or three working together. Approach: add all rates, then invert the sum.

Type 2: Finding an Unknown Rate

Given the combined time and one individual time, find the other individual time. Approach: subtract the known rate from the combined rate to get the unknown rate.

Type 3: Departure Problem

A and B work together for n days, then one worker leaves. Find how many more days the other needs to finish.

Approach: combined rate multiplied by n gives work done; 1 minus that is remaining work; remaining work divided by the individual rate gives additional days.

Type 4: Men-Days (Workforce Changes)

Total work stays constant in man-days. Scale workers and time inversely.

Formula: Men1 multiplied by Days1 equals Men2 multiplied by Days2.

If 8 men finish in 12 days (96 man-days total), then 6 men need 96 divided by 6 = 16 days.

Solved Examples: Beginner to Moderate

All examples below are derived from first principles. Answers have been verified independently.

Example 1: Two Workers Together

• Given: A completes a job in 10 days. B completes the same job in 15 days.
• Find: Days for A and B working together.
• Step 1: LCM(10, 15) = 30. A’s rate = 3/30; B’s rate = 2/30.
• Step 2: Combined rate = 5/30 = 1/6.
• Step 3: Combined time = 6 days.
• Answer: 6 days.

Example 2: Three Workers Together

• Given: A, B, and C take 10, 15, and 20 days individually.
• Find: Time for all three working together.
• Step 1: LCM(10, 15, 20) = 60. Rates: A = 6/60, B = 4/60, C = 3/60.
• Step 2: Combined rate = 13/60.
• Step 3: Combined time = 60/13 days (approximately 4.6 days).
• Answer: 60/13 days.

Example 3: Finding an Unknown Rate

• Given: A and B together finish a job in 10 days. A alone finishes in 15 days.
• Find: B’s time alone.
• Step 1: Combined rate = 1/10. A’s rate = 1/15.
• Step 2: LCM(10, 15) = 30. B’s rate = 3/30 minus 2/30 = 1/30.
• Step 3: B alone takes 30 days.
• Answer: 30 days.

Example 4: Men-Days Scaling

• Given: 8 men complete a job in 12 days.
• Find: Time for 6 men to complete the same job.
• Step 1: Total work = 8 multiplied by 12 = 96 man-days.
• Step 2: Time for 6 men = 96 divided by 6 = 16 days.
• Answer: 16 days.

Example 5: Three Workers, One Unknown Rate

• Given: A, B, and C together finish in 6 days. A alone in 12 days. B alone in 18 days.
• Find: C’s time alone.
• Step 1: LCM(6, 12, 18) = 36. Combined rate = 6/36; A’s rate = 3/36; B’s rate = 2/36.
• Step 2: C’s rate = 6/36 minus 3/36 minus 2/36 = 1/36.
• Step 3: C alone takes 36 days.
• Answer: 36 days.

Example 6: Departure Problem

• Given: A takes 16 days alone. B takes 24 days alone. They work together for 4 days, then A leaves.
• Find: How many more days does B need to finish the job?
• Step 1: LCM(16, 24) = 48. A’s rate = 3/48; B’s rate = 2/48. Combined = 5/48.
• Step 2: Work done in 4 days = 4 multiplied by 5/48 = 20/48 = 5/12.
• Step 3: Remaining work = 1 minus 5/12 = 7/12.
• Step 4: B alone: (7/12) divided by (1/24) = (7/12) multiplied by 24 = 14 days.
• Answer: 14 more days.
• Verification: B’s total days = 4 + 14 = 18. Work by B = 18/24 = 3/4. Work by A = 4/16 = 1/4. Total = 1. Correct.

Example 7: Workforce Expansion Mid-Job

• Given: A contractor hires 10 workers for a job. After 10 days, 5 more workers join. The total job requires 400 worker-days.
• Find: How many additional days are needed after day 10?
• Step 1: Work done in first 10 days = 10 multiplied by 10 = 100 worker-days.
• Step 2: Remaining = 400 minus 100 = 300 worker-days.
• Step 3: With 15 workers: 300 divided by 15 = 20 additional days.
• Answer: 20 more days.

Intermediate Problems

These examples combine multiple steps or involve efficiency ratios.

Example 8: Efficiency Ratio

• Given: A finishes a job in 10 days. B is 50% more efficient than A.
• Find: B’s time alone.
• Step 1: A’s rate = 1/10 per day.
• Step 2: B’s rate = 1.5 multiplied by (1/10) = 15/100 = 3/20 per day.
• Step 3: B’s time = 20/3 days (approximately 6.67 days).
• Answer: 20/3 days.

Example 9: Adding a Third Worker to an Existing Pair

• Given: A and B together finish a job in 12 days. When C joins them, all three finish in 8 days.
• Find: C’s time alone.
• Step 1: A and B’s combined rate = 1/12.
• Step 2: A, B, and C’s combined rate = 1/8.
• Step 3: C’s rate = 1/8 minus 1/12. LCM(8, 12) = 24. C’s rate = 3/24 minus 2/24 = 1/24.
• Step 4: C alone takes 24 days.
• Answer: 24 days.

Example 10: Workers Leave Before Completion

• Given: A project requires 720 man-days. 30 workers start. After 6 days, 10 workers leave.
• Find: Total days to complete the project.
• Step 1: Work done in first 6 days = 30 multiplied by 6 = 180 man-days.
• Step 2: Remaining = 720 minus 180 = 540 man-days.
• Step 3: With 20 workers remaining: 540 divided by 20 = 27 more days.
• Step 4: Total = 6 + 27 = 33 days.
• Answer: 33 days.

Pipes and Cisterns

Pipes and cisterns is Time and Work with a physical context swap. The algebra is identical. A filling pipe contributes a positive rate. A drain contributes a negative rate. Find the net rate, then invert for total time.

The one mistake students make: forgetting to treat the drain as subtraction and instead adding all three rates. Double-check the sign for every emptying pipe before calculating.

Example 11: Mixed Fill and Drain

• Given: Pipe X fills a tank in 10 hours. Pipe Y fills it in 15 hours. Pipe Z drains it in 30 hours. All three are open simultaneously.
• Find: Time to fill the tank.
• Step 1: LCM(10, 15, 30) = 30. X’s rate = 3/30 per hour; Y’s rate = 2/30 per hour; Z’s drain rate = 1/30 per hour (subtracted).
• Step 2: Net rate = (3 + 2 minus 1) / 30 = 4/30 = 2/15 per hour.
• Step 3: Time to fill = 15/2 = 7.5 hours.
• Answer: 7.5 hours.

A common error on this type: rounding 7.5 to 8. Campus test answer keys do not round it. 7.5 hours is the exact answer.

Preparing Efficiently for Placement Tests

Campus aptitude tests allocate 2 to 4 questions to Time and Work and Pipes and Cisterns combined. The questions follow the five types covered above, so pattern recognition matters more than raw calculation speed.

Practical approach for the test:

• Identify the type first (combined rate, departure, men-days, pipes). Classifying takes 20 to 30 seconds and prevents wrong-path calculations.
• For every workforce problem, write the total man-days before doing anything else. That single anchor number prevents the most common errors.
• Keep denominators in LCM form throughout the calculation. Converting to simplest form mid-step invites errors.
• If the answer options are whole numbers but your calculation gives a fraction, re-read the question. It likely asks for additional days rather than total days, and the subtraction is the step that was missed.

For how Time and Work fits into the full placement test structure alongside logical reasoning and verbal ability, the campus placement evaluation test guide covers section breakdowns and preparation timelines. The placement preparation book guide lists the standard titles used in most coaching programmes. Mu Sigma weights quantitative reasoning heavily in its dedicated aptitude round. The Mu Sigma MuApt analysis maps exactly how pattern-recognition problems appear in analytics-company hiring. IndiaBix Time and Work has questions in the same format as campus tests. The TCS NQT careers page links to official preparation resources.

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