SSC CGL 2027 Time and Work Questions with Efficiency Comparison

Time and Work is an important topic in Quantitative Aptitude for SSC CGL preparation. Questions from this chapter commonly involve work efficiency, the time taken by individuals to complete a task, combined work, and comparisons between workers. Learning how to compare efficiency can make many calculations faster and easier.

In this guide, you will learn the basic Time and Work formulas, efficiency comparison methods, shortcut techniques, solved examples, and practice questions with answers. These concepts will help you build a stronger foundation for SSC CGL 2027 Quantitative Aptitude preparation.

1. Basic Concepts of Time and Work

Time and Work questions examine how long a person or group takes to complete a task. If a person completes a job in a fixed number of days, we can calculate the fraction of work completed in one day.

For example, if A completes a job in 10 days, A completes one-tenth of the work in one day, assuming a constant working rate.

These formulas assume that the working rate remains constant throughout the task.

2. Understanding Work Efficiency

Efficiency refers to the amount of work completed in a given period. A person who completes the same task in fewer days has a higher work rate and greater efficiency.

If A completes a job in 10 days and B completes the same job in 15 days, A is more efficient than B.

Their efficiencies are inversely proportional to the time they take:

Solved Example 1: Comparing Efficiency

Question: A can complete a job in 12 days, while B can complete the same job in 18 days. Find the ratio of their efficiencies.

Solution:

Efficiency of A : Efficiency of B = 1/12 : 1/18.

Taking the LCM of 12 and 18, we obtain:

Efficiency ratio = 18 : 12 = 3 : 2.

Answer: 3:2. A is 1.5 times as efficient as B.

3. Combined Work Formula

When two people work together, their individual work rates are added, provided both contribute to the same task at constant rates.

If A completes a job in x days and B completes it in y days, their combined one-day work is:

Solved Example 2: A and B Working Together

Question: A can complete a job in 12 days and B can complete it in 18 days. How many days will they take to complete the job together?

Solution:

Combined time = (12 × 18) ÷ (12 + 18).

= 216 ÷ 30.

= 7.2 days.

Answer: 7.2 days, or 7⅕ days.

Efficiency method: Take total work as the LCM of 12 and 18, which is 36 units.

• A's efficiency = 36 ÷ 12 = 3 units per day.
• B's efficiency = 36 ÷ 18 = 2 units per day.
• Combined efficiency = 3 + 2 = 5 units per day.

Time taken = 36 ÷ 5 = 7.2 days.

4. Efficiency Comparison Using Total Work

In many examination questions, choosing a convenient total work value helps avoid fractions. When individual completion times are given, their LCM is often a useful choice for total work.

Solved Example 3: Finding Time from an Efficiency Ratio

Question: A is twice as efficient as B. If B completes a job in 20 days, how many days will A take?

Solution:

A's efficiency : B's efficiency = 2:1.

Time ratio is the inverse, so A's time : B's time = 1:2.

A's time = 20 × 1/2 = 10 days.

Answer: 10 days.

Solved Example 4: Efficiency Difference

Question: A can complete a job in 15 days and B can complete it in 20 days. If the total work is taken as 60 units, compare their daily efficiencies.

Solution:

Total work = LCM of 15 and 20 = 60 units.

A's efficiency = 60 ÷ 15 = 4 units per day.

B's efficiency = 60 ÷ 20 = 3 units per day.

Efficiency ratio = 4:3.

Answer: A and B have an efficiency ratio of 4:3.

5. Work and Number of Workers

When all workers have the same efficiency and work for the same number of hours each day, the amount of work is directly proportional to the number of workers and the number of days.

Solved Example 5: Workers and Days

Question: Twelve workers can complete a job in 15 days. How many days will 20 workers take if everyone works at the same rate?

Solution:

12 × 15 = 20 × x.

180 = 20x.

x = 9 days.

Answer: 9 days.

6. When One Person Joins or Leaves

Some questions involve one worker starting a task and another joining later, or a worker leaving before the task is completed. Calculate the work completed in each stage separately and then add the fractions of work.

Solved Example 6: Working in Two Stages

Question: A can complete a job in 10 days. A works alone for 4 days, after which the remaining work is completed by B alone in 9 days. How long would B take to complete the entire job alone?

Solution:

A's one-day work = 1/10.

Work completed by A in 4 days = 4/10 = 2/5.

Remaining work = 1 − 2/5 = 3/5.

B completes 3/5 of the work in 9 days.

B's one-day work = (3/5) ÷ 9 = 1/15.

Answer: B would complete the entire job in 15 days.

7. Important Shortcuts for SSC CGL

• Use the LCM method: When completion times are given, use their LCM as total work to simplify daily work calculations.
• Reverse the time ratio: Efficiency and time are inversely proportional for the same task.
• Add work rates: When people work together on the same job, add their individual rates.
• Subtract remaining work: For multi-stage questions, calculate completed work before finding the remaining fraction.
• Check the assumptions: Worker-based shortcuts require comparable working hours and constant efficiency.
• Verify the final time: A group working together should generally finish faster than either person working alone when both contribute positively.

8. Common Mistakes to Avoid

1. Assuming that the person who takes more days is more efficient.
2. Adding completion times instead of adding work rates.
3. Using a direct time ratio when an inverse ratio is required.
4. Forgetting to subtract the work already completed.
5. Applying the workers-and-days formula when workers have different efficiencies without adjusting for those differences.

9. Practice Questions for SSC CGL 2027

Try these questions before checking the answer key.

Answer Key with Explanations

1. B) 3:2: Efficiency ratio = 1/16 : 1/24 = 24:16 = 3:2.

2. B) 6 days: Combined time = (10 × 15) ÷ (10 + 15) = 150/25 = 6 days.

3. B) 8 days: A is three times as efficient as B, so A takes one-third of B's time: 24 ÷ 3 = 8 days.

4. B) 9 days: Workers × Days = Constant. 15 × 12 = 20 × x, so x = 9 days.

5. C) 1/2: Combined one-day work = 1/12 + 1/18 = 5/36. In 3 days, they complete 3 × 5/36 = 15/36 = 5/12. Therefore, the correct option is B) 5/12.

10. How to Prepare Time and Work for SSC CGL

Start by learning how to calculate one-day work and how to convert completion times into efficiency ratios. Next, practise combined work, worker-and-day problems, and questions where one person joins or leaves during a task.

Use timed practice sets to improve speed, but prioritise accuracy first. Maintain a notebook of formulas and review the mistakes you make while calculating fractions, efficiency ratios, and remaining work.

Check the official SSC CGL notification and syllabus when released for the applicable 2027 examination details. This article is a preparation resource and does not guarantee that a particular question will appear in the examination.

Frequently Asked Questions

1. What is the basic formula for Time and Work?

Work equals work rate multiplied by time. If the whole job is taken as one unit, one-day work is the reciprocal of the number of days required.

2. How do you compare the efficiencies of two people?

For the same task, efficiency is inversely proportional to time. If A takes x days and B takes y days, their efficiency ratio is y:x.

3. How do you calculate combined work?

Add the individual work rates and divide the total work by the combined rate to find the time required.

4. What is the LCM method in Time and Work?

Choose the LCM of the given completion times as the total work. This often converts individual daily work into whole numbers.

5. How can I solve Time and Work questions faster?

Practise efficiency ratios, combined work rates, and the LCM method. Review each incorrect answer to identify calculation errors.