Master Time and Work for SSC CGL & CHSL: Concepts, Tricks & Solved Questions

Introduction to Time and Work for SSC Exams

Welcome, SSC aspirants! In your journey to crack the SSC CGL and CHSL exams, the Quantitative Aptitude section stands as a critical pillar. Among its many topics, 'Time and Work' is a perennial favorite of examiners. You can expect to find 2-3 questions from this chapter in both Tier-1 and Tier-2 exams, making it a high-scoring area if your concepts are clear. This topic tests your logical thinking and ability to work with fractions and ratios under pressure.

This comprehensive guide is designed to take you from the basic concepts of Time and Work to solving complex problems with speed and accuracy. We will cover fundamental principles, essential formulas, time-saving shortcuts like the LCM method, and a wide array of solved examples and practice questions tailored specifically for the SSC pattern. By the end of this post, you'll have the confidence and skills to tackle any Time and Work question that comes your way.

Fundamental Concepts of Time and Work

To master this topic, you must first understand the three core components: Work, Time, and Efficiency.

• Work: This is the task or the job that needs to be completed. In most problems, if the amount of work is not specified, it is assumed to be 1 unit.
• Time: This is the duration taken to complete the work. It can be measured in days, hours, minutes, etc.
• Efficiency (or Rate of Work): This is the amount of work an individual can do in a unit of time (e.g., work done per day or per hour). Efficiency is the cornerstone of solving Time and Work problems quickly.

The fundamental relationship that connects these three is:

Work = Efficiency × Time

From this, we can derive:

• Efficiency = Work / Time
• Time = Work / Efficiency

A crucial takeaway is that Efficiency is inversely proportional to the Time taken to complete the same amount of work. If someone is more efficient, they will take less time, and vice versa.

Example: If Ram is twice as efficient as Shyam, he will take half the time Shyam takes to complete the same job.

Key Formulas and Methods for Time and Work

While understanding concepts is key, knowing the right methods and formulas can drastically reduce your solving time. Let's explore the most effective techniques.

1. The Unitary Method (Fraction Method)

This is the most basic method. If a person 'A' can finish a piece of work in 'X' days, then the work done by 'A' in one day is 1/X.

Formula for two persons working together: If A can do a work in X days and B can do it in Y days, then the time taken by A and B together is:

Time = (X * Y) / (X + Y) days

2. The LCM Method (Efficiency Method)

This is the most popular and efficient method for solving Time and Work problems. It avoids complex fractions and makes calculations much simpler.

Steps:

1. Step 1: Take the LCM (Least Common Multiple) of the time taken by each individual. This LCM represents the Total Work in units.
2. Step 2: Calculate the efficiency of each individual using the formula: Efficiency = Total Work / Time Taken. This gives you the work done per day (or per hour) in units.
3. Step 3: Use the efficiencies to solve the problem as required. For example, to find the time taken when they work together, use: Time = Total Work / Combined Efficiency.

3. The MDH Formula

This formula is used when you have groups of people working for a certain number of days and hours. It's based on the concept of 'man-days' or 'man-hours'.

The core formula is: M1 * D1 * H1 / W1 = M2 * D2 * H2 / W2

Here is a breakdown of the variables:

You only use the variables given in the question. For example, if hours aren't mentioned, the formula simplifies to: M1 * D1 / W1 = M2 * D2 / W2.

4. Work and Wages

A simple principle governs the distribution of wages: Wages are distributed in proportion to the work done by each individual. Since the work done is a product of efficiency and time, if the time is constant for everyone, wages are distributed in the ratio of their efficiencies.

Ratio of Wages of A : B = Ratio of Work done by A : B

Solved Examples: Applying Time and Work Concepts

Let's solidify our understanding with some typical SSC CGL/CHSL level questions.

Example 1: Basic Concept (Working Together)

Question: A can complete a work in 10 days and B can complete the same work in 15 days. In how many days will they complete the work if they work together?

Solution (Using LCM Method):

• Step 1: Find the LCM of the times. LCM(10, 15) = 30. Let this be the Total Work (30 units).
• Step 2: Calculate individual efficiencies.
  • A's Efficiency = Total Work / Time = 30 / 10 = 3 units/day.
  • B's Efficiency = Total Work / Time = 30 / 15 = 2 units/day.
• Step 3: Calculate their combined efficiency.
  • Combined Efficiency (A + B) = 3 + 2 = 5 units/day.
• Step 4: Find the time taken together.
  • Time = Total Work / Combined Efficiency = 30 / 5 = 6 days.

Answer: They will complete the work in 6 days together.

Example 2: Work with Three Persons

Question: A, B, and C can do a job in 12, 15, and 20 days respectively. How many days will they take to finish the job if they work together?

Solution (Using LCM Method):

• Total Work: LCM(12, 15, 20) = 60 units.
• Efficiencies:
  • A's Efficiency = 60 / 12 = 5 units/day.
  • B's Efficiency = 60 / 15 = 4 units/day.
  • C's Efficiency = 60 / 20 = 3 units/day.
• Combined Efficiency (A + B + C): 5 + 4 + 3 = 12 units/day.
• Time Taken Together: Total Work / Combined Efficiency = 60 / 12 = 5 days.

Answer: They will complete the work in 5 days.

Example 3: MDH Formula Application

Question: If 15 men can build a wall 100 meters long in 10 days, how many men will be required to build a similar wall 180 meters long in 9 days?

Solution:

• Here, we use the formula: M1 * D1 / W1 = M2 * D2 / W2
• Given:
  • M1 = 15 men
  • D1 = 10 days
  • W1 = 100 meters
  • M2 = ?
  • D2 = 9 days
  • W2 = 180 meters
• Applying the formula:
• (15 * 10) / 100 = (M2 * 9) / 180
• 150 / 100 = (M2 * 9) / 180
• 1.5 = M2 / 20
• M2 = 1.5 * 20 = 30

Answer: 30 men will be required.

Example 4: Work and Efficiency Ratio

Question: A is twice as good a workman as B, and together they finish a piece of work in 14 days. In how many days can A alone finish the work?

Solution:

• Efficiency Ratio: Since A is twice as good as B, the ratio of their efficiencies is A : B = 2 : 1.
• Let A's efficiency be 2 units/day and B's efficiency be 1 unit/day.
• Combined Efficiency (A + B): 2 + 1 = 3 units/day.
• They finish the work in 14 days together. So, Total Work = Combined Efficiency × Time = 3 * 14 = 42 units.
• Time taken by A alone: Time = Total Work / A's Efficiency = 42 / 2 = 21 days.

Answer: A alone can finish the work in 21 days.

Example 5: Leaving/Joining Work

Question: A and B can do a work in 18 and 24 days respectively. They started the work together, but B left 4 days before the completion of the work. In how many days was the work completed?

Solution:

• Total Work: LCM(18, 24) = 72 units.
• Efficiencies:
  • A's Efficiency = 72 / 18 = 4 units/day.
  • B's Efficiency = 72 / 24 = 3 units/day.
• B left 4 days before completion. This means A worked alone for the last 4 days.
• Work done by A in the last 4 days: 4 * 4 = 16 units.
• Remaining Work (done by A and B together): 72 - 16 = 56 units.
• Time taken by A and B to do this remaining work: Time = Work / Combined Efficiency = 56 / (4 + 3) = 56 / 7 = 8 days.
• Total time to complete the work: 8 days (together) + 4 days (A alone) = 12 days.

Answer: The work was completed in 12 days.

Practice Questions for SSC CGL & CHSL Aspirants

Now it's your turn to practice. Try to solve these questions using the methods discussed above.

1. A can do a piece of work in 20 days and B in 30 days. They work together for 7 days and then both leave the work. Then C alone finishes the remaining work in 10 days. In how many days will C finish the full work?
2. A and B can do a work in 12 days, B and C in 15 days, and C and A in 20 days. How long would A alone take to do the work?
3. 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?
4. 20 women can do a work in 16 days. 16 men can complete the same work in 15 days. What is the ratio between the capacity of a man and a woman?
5. A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in how many days?
6. A and B undertake to do a piece of work for Rs. 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 C.
7. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
8. A and B start working on a job, but A leaves after 4 days. B continues and finishes the remaining work in 9 days. If A could complete the job in 12 days, in how many days B alone can finish the entire job?
9. 12 men can complete a work in 8 days. 16 women can complete the same work in 12 days. 8 men and 8 women started working and worked for 6 days. How many more men are to be added to complete the remaining work in 1 day?
10. A works on Monday, B works on Tuesday, C works on Wednesday and so on. A can do a job in 36 days, B in 18 days, and C in 24 days. How many days will it take to complete the job?

Solutions to Practice Questions

Solution 1:

Total Work = LCM(20, 30) = 60 units. A's efficiency = 3, B's efficiency = 2. Combined = 5 units/day. Work done in 7 days = 7 * 5 = 35 units. Remaining work = 60 - 35 = 25 units. C does 25 units in 10 days, so C's efficiency = 25/10 = 2.5 units/day. Time for C to do full work = 60 / 2.5 = 24 days. Answer: 24 days

Solution 2:

Total Work = LCM(12, 15, 20) = 60 units. Eff(A+B) = 5, Eff(B+C) = 4, Eff(C+A) = 3. Adding them: 2(A+B+C) = 12, so Eff(A+B+C) = 6. To find A's efficiency: Eff(A) = Eff(A+B+C) - Eff(B+C) = 6 - 4 = 2. Time for A alone = 60 / 2 = 30 days. Answer: 30 days

Solution 3:

Efficiency ratio A:B = 130:100 = 13:10. Total Work = Eff(A) * Time(A) = 13 * 23 = 299 units. Combined efficiency = 13 + 10 = 23. Time together = 299 / 23 = 13 days. Answer: 13 days

Solution 4:

Work done by 20 women in 16 days = Work done by 16 men in 15 days. 20W * 16 = 16M * 15. 20W = 15M. 4W = 3M. M/W = 4/3. Ratio Man:Woman = 4:3. Answer: 4:3

Solution 5:

Total Work = LCM(24, 6, 12) = 24 units. Eff(A)=1, Eff(B)=4, Eff(C)=2. Combined efficiency = 1+4+2 = 7. Time together = 24/7 days. Answer: 3 3/7 days

Solution 6:

Total Work = LCM(6, 8, 3) = 24 units. Eff(A)=4, Eff(B)=3, Eff(A+B+C)=8. So, Eff(C) = 8 - (4+3) = 1. Wages are in the ratio of efficiency A:B:C = 4:3:1. C's share = (1 / (4+3+1)) * 600 = (1/8) * 600 = Rs. 75. Answer: Rs. 75

Solution 7:

This is a Pipes and Cisterns problem, which follows the same logic. Total Work (Capacity) = LCM(20, 30) = 60 units. Eff(A)=3, Eff(B)=2. Combined = 5. Time together = 60 / 5 = 12 minutes. Answer: 12 minutes

Solution 8:

Total Work = 12 units (based on A's time). A's efficiency = 1 unit/day. Work done by A in 4 days = 4 * 1 = 4 units. Remaining work = 12 - 4 = 8 units. B does these 8 units in 9 days. So, B's efficiency = 8/9 units/day. Time for B to do the whole job = 12 / (8/9) = (12*9)/8 = 27/2 = 13.5 days. Answer: 13.5 days

Solution 9:

Total Work = 12M * 8D = 96 Man-Days. Also, Total Work = 16W * 12D = 192 Woman-Days. So, 96M = 192W => 1M = 2W. Convert everything to men. 8M + 8W = 8M + 4M = 12M. Work done in 6 days = 12M * 6D = 72 Man-Days. Remaining Work = 96 - 72 = 24 Man-Days. This needs to be done in 1 day, so 24 men are required. We already have 8M+8W = 12 Men. So, we need 24 - 12 = 12 more men. Answer: 12 men

Solution 10:

Total Work = LCM(36, 18, 24) = 72 units. Eff(A)=2, Eff(B)=4, Eff(C)=3. Work in a 3-day cycle (A+B+C) = 2+4+3 = 9 units. To reach 72 units, we need 72/9 = 8 such cycles. Total days = 8 cycles * 3 days/cycle = 24 days. Answer: 24 days

Conclusion and Preparation Tips

Time and Work is a predictable and logical topic. Once you internalize the core concepts, especially the LCM method, you can solve most problems with ease. Here are some final tips to ace this topic:

• Master the LCM Method: It is faster and less prone to calculation errors than the fraction method. Practice it until it becomes second nature.
• Understand Ratios: Many efficiency-based problems are simply applications of ratios. A strong grasp of the Ratio and Proportion chapter will help immensely.
• Practice Regularly: Consistency is key. Solve at least 5-10 Time and Work problems daily from previous year papers and mock tests.
• Analyze Patterns: Pay attention to recurring question patterns like 'work and wages', 'alternate days', and 'worker leaves/joins'.

By dedicating sincere effort to understanding and practicing this topic, you can easily secure full marks and take a significant step towards clearing the SSC CGL and CHSL exams. Good luck!