How to Solve Time and Work Problems

How to Solve Time and Work Problems

(For SSC, Bank, Railway Exams – Ace Your Exam with Confidence!)

Introduction

"Master Time and Work problems, and you’ll unlock 3–5 easy marks in every SSC, Bank, or Railway exam—marks that decide whether you clear the cutoff or not!

(On camera: Hold up a past paper with a Time and Work question circled.) "This one question type appears in almost every competitive exam. If you skip it, you’re leaving free marks on the table. Today, I’ll show you a foolproof 4-step method to solve any Time and Work problem in under 60 seconds—even if you hate math!

What You Need To Know First

Before diving in, make sure you understand these 3 prerequisites: 1. Basic fractions and percentages – You’ll need to add, subtract, and compare fractions quickly. 2. Unitary method – Finding the value of "1 unit" (e.g., if 5 workers finish a job in 10 days, how much does 1 worker do in 1 day?). 3. LCM (Least Common Multiple) – Used to simplify work rates (you’ll see why in Step 2).

(On camera: Pause and ask:) "If any of these feel rusty, pause now and review them—this guide will make 10x more sense!

Key Vocabulary

(On camera: Point to the table and say:) "Memorize these terms—they’re the language of Time and Work problems. If you don’t know what ‘work rate’ means, the problem will feel like gibberish!

Formulas To Know

(Write these on a whiteboard or display on screen.)

1. Basic Work Formula
   [
   \text{Work} = \text{Work Rate} \times \text{Time}
   ]
2. Work = Total job (usually "1" for one complete task).
3. Work Rate = Fraction of work done per unit time (e.g., 1/10 per day).
4. Time = Time taken to complete the work.

5. MEMORISE THIS – This is the foundation of every problem.

6. Combined Work Rate (When working together)
   [
   \text{Combined Rate} = \text{Rate of A} + \text{Rate of B} + \text{Rate of C} + \dots
   ]

7. If A’s rate = 1/10 and B’s rate = 1/15, then combined rate = 1/10 + 1/15 = 1/6.

8. MEMORISE THIS – You’ll use it in 90% of problems.

9. Time Taken Together
   [
   \text{Time} = \frac{\text{Total Work}}{\text{Combined Rate}}
   ]

10. If combined rate = 1/6, time to complete 1 work = 1 / (1/6) = 6 days.

11. MEMORISE THIS – This flips the combined rate into time.

12. Efficiency Ratio (When given "A is twice as fast as B")
    [
    \text{Rate of A} : \text{Rate of B} = 2 : 1
    ]

13. If B’s rate = x, then A’s rate = 2x.

14. Given on exam sheet? Sometimes, but memorize the logic.

15. Negative Work (Leaks, Pipes, etc.)
    [
    \text{Net Rate} = \text{Filling Rate} - \text{Emptying Rate}
    ]

16. Example: Pipe fills at 1/4 per hour, leak empties at 1/6 per hour → Net rate = 1/4 - 1/6 = 1/12 per hour.
17. MEMORISE THIS – Common in tank/pipe problems.

(On camera: Circle the first 3 formulas and say:) "These three are your bread and butter. If you forget everything else, remember these!

Step-by-Step Method

(On camera: Write these steps on a board or display them one by one.)

Step 1: Identify the Total Work

• Assume the total work is "1 unit" (e.g., 1 wall, 1 tank, 1 project).
• If the problem gives a specific number (e.g., "digging 100 meters"), treat that as the total work.

Step 2: Find Individual Work Rates

• Work Rate = 1 / Time taken alone
• If A takes 10 days to finish the work alone, A’s rate = 1/10 per day.
• If B takes 15 days, B’s rate = 1/15 per day.
• Pro Tip: If the problem gives efficiency ratios (e.g., "A is 50% faster than B"), adjust the rates accordingly.
• Example: If B’s rate = x, A’s rate = 1.5x.

Step 3: Calculate Combined Work Rate

• Add the individual rates of all workers/machines working together.
• Combined rate = Rate of A + Rate of B + Rate of C + ...
• If someone is undoing work (e.g., a leak), subtract their rate.
• Example: Pipe fills at 1/4, leak empties at 1/6 → Net rate = 1/4 - 1/6 = 1/12.

Step 4: Find Time Taken Together

• Time = Total Work / Combined Rate
• If combined rate = 1/6 per day, time to complete 1 work = 1 / (1/6) = 6 days.
• If the problem asks for partial work (e.g., "How much work in 3 days?"), multiply rate × time.
• Example: Combined rate = 1/6 → Work in 3 days = (1/6) × 3 = 1/2.

(On camera: Pause and say:) "That’s it! Four steps. No shortcuts, no guesswork. Let’s see this in action with an example."

Worked Examples

Example 1 – Basic

Problem: A can complete a job in 10 days. B can complete the same job in 15 days. How long will it take if they work together?

Solution (Using the 4 Steps):

1. Identify Total Work

2. Total work = 1 job.

3. Find Individual Work Rates

4. A’s rate = 1/10 per day.

5. B’s rate = 1/15 per day.

6. Calculate Combined Work Rate

7. Combined rate = 1/10 + 1/15.
8. LCM of 10 and 15 = 30.

9. Combined rate = (3 + 2)/30 = 5/30 = 1/6 per day.

10. Find Time Taken Together

11. Time = Total Work / Combined Rate = 1 / (1/6) = 6 days.

Answer: 6 days.

What we did and why: - We treated the job as "1 unit" to simplify calculations. - We added the rates because A and B are working together. - We used LCM to add fractions quickly—this saves time in exams!

Example 2 – Medium (Efficiency Given)

Problem: A is twice as efficient as B. Together, they finish a job in 12 days. How long will A take alone?

Solution:

1. Identify Total Work

2. Total work = 1 job.

3. Find Individual Work Rates

4. Let B’s rate = x per day.

5. A is twice as efficient → A’s rate = 2x per day.

6. Calculate Combined Work Rate

7. Combined rate = A’s rate + B’s rate = 2x + x = 3x per day.
8. Given: Together they take 12 days → Combined rate = 1/12 per day.
9. So, 3x = 1/12 → x = 1/36.

10. Therefore, A’s rate = 2x = 2/36 = 1/18 per day.

11. Find Time Taken by A Alone

12. Time = Total Work / A’s Rate = 1 / (1/18) = 18 days.

Answer: 18 days.

What we did and why: - We used a variable (x) to represent B’s rate because efficiency was given as a ratio. - We set up an equation using the combined rate to solve for x. - This is a common "efficiency ratio" problem—practice these!

Example 3 – Exam-Style (Negative Work)

Problem: A pipe can fill a tank in 4 hours. A leak at the bottom can empty the tank in 6 hours. If both the pipe and the leak are open, how long will it take to fill the tank?

Solution:

1. Identify Total Work

2. Total work = 1 tank.

3. Find Individual Work Rates

4. Pipe’s filling rate = 1/4 per hour.

5. Leak’s emptying rate = 1/6 per hour.

6. Calculate Combined Work Rate

7. Net rate = Filling rate - Emptying rate = 1/4 - 1/6.
8. LCM of 4 and 6 = 12.

9. Net rate = (3 - 2)/12 = 1/12 per hour.

10. Find Time Taken to Fill the Tank

11. Time = Total Work / Net Rate = 1 / (1/12) = 12 hours.

Answer: 12 hours.

What we did and why: - We treated the leak as negative work and subtracted its rate. - This is a classic "pipe and tank" problem—examiners love these! - Always check if work is being added or subtracted.

Common Mistakes

(On camera: Hold up a red marker and say:) "These mistakes cost students marks every year. Don’t be one of them!

Exam Traps

(On camera: Lean in and say:) "Examiners don’t just test your math—they test your attention to detail. Here’s how they trick you:"

1-Minute Recap

(On camera: Speak naturally, as if to a friend the night before the exam.)

"Okay, listen up—this is your last-minute cheat sheet for Time and Work problems:

1. Total work = 1 unit. Always start here.
2. Work rate = 1 / time alone. If A takes 10 days, A’s rate = 1/10 per day.
3. Add rates for combined work. A + B = 1/10 + 1/15 = 1/6 → 6 days together.
4. Subtract rates for negative work. Pipe fills at 1/4, leak empties at 1/6 → Net rate = 1/12 → 12 hours.
5. Watch for efficiency ratios. If A is twice as fast as B, A’s rate = 2 × B’s rate.
6. Never add times! 10 days + 15 days ≠ 25 days. Add rates instead.
7. Check units. Hours vs. days? Convert first!

That’s it. Four steps, seven rules. Go into that exam, solve every Time and Work problem in under a minute, and grab those 3–5 easy marks. You’ve got this!