ssc gd time and work questions

• The Basics of Work and Time (Efficiency)
• Combined Work (Working Together)
• Finding the Time Taken (The Unitary Method)
• Pipes and Cisterns (Tanks and Taps)

---

The Basics of Work and Time (Efficiency)

What is Time and Work?

This topic, ssc gd time and work, is about how long it takes people or machines to finish a job.

• Work: The total task you need to finish (like building a wall or eating a pizza).
• Time: How many days, hours, or minutes it takes.
• Efficiency: How fast someone works. A person with high efficiency finishes the work quickly.

The Main Rule: Work is always considered ‘1’ (or 100%) when it is finished.

Key Formula: $$\text{Work Done in 1 Day}=\frac{1}{\text{Total Time Taken}}$$

If A takes 5 days to finish a job, A does $\frac{1}{5}$ of the job every day. This is A’s daily efficiency. These ssc gd time and work questions often test this basic idea.

Solved Examples

Example 1: Finding Daily Work

Ravi can paint a room in 8 days. How much work does Ravi do in one day?

Solution:

1. First, let’s understand what we need to find: We need Ravi’s daily work, which is his efficiency.
2. Now, write down the formula: Daily Work $=\frac{1}{\text{Total Time}}$
3. Put the numbers in: Ravi takes 8 days. $$\text{Daily Work}=\frac{1}{8}$$
4. Calculate it: Ravi finishes $\frac{1}{8}$ of the room painting every day.
5. So, the answer is: $\frac{1}{8}$ of the work.

Example 2: Finding Total Time from Daily Work

If Sita finishes $\frac{1}{12}$ of a task every day, how many days will she take to complete the whole task?

Solution:

1. First, let’s understand what we need to find: We need the total time (T).
2. Now, write down the formula: Total Time $=\frac{1}{\text{Daily Work}}$
3. Put the numbers in: Sita’s daily work is $\frac{1}{12}$. $$\text{Total Time}=\frac{1}{\frac{1}{12}}$$
4. Calculate it: When you divide by a fraction, you flip it and multiply. $$\text{Total Time}=1\times 12=12\text{ days}$$
5. So, the answer is: 12 days. This is a simple type of time and work ssc gd questions.

Example 3: Comparing Efficiency

A is twice as efficient as B. If B takes 30 days to finish a job, how many days will A take?

Solution:

1. First, let’s understand what we need to find: We need A’s time. Efficiency and Time are opposite (inversely proportional). If you are faster (more efficient), you take less time.
2. Find B’s time: B takes 30 days.
3. Use the efficiency ratio: A is 2 times faster than B.
4. Calculate A’s time: A will take half the time B takes. $$\text{A’s Time}=\frac{\text{B’s Time}}{2}=\frac{30}{2}=15\text{ days}$$
5. So, the answer is: 15 days.

Example 4: The LCM Method (Total Work)

Ramesh takes 10 days and Suresh takes 15 days to complete a job. Find the total work unit.

Solution:

1. First, let’s understand what we need to find: We need a common number that both 10 and 15 can divide easily. This number is called the Total Work Unit (LCM).
2. Find the LCM of 10 and 15:
   • Multiples of 10: 10, 20, 30, 40…
   • Multiples of 15: 15, 30, 45…
3. The LCM is 30. We assume the total work is 30 units (e.g., making 30 toys).
4. Calculate daily efficiency (units per day):
   • Ramesh’s efficiency: $\frac{30}{10}=3$ units/day.
   • Suresh’s efficiency: $\frac{30}{15}=2$ units/day.
5. So, the answer is: The Total Work Unit is 30. This LCM method makes solving ssc gd time and work questions pdf much easier.

---

Combined Work (Working Together)

How People Work Together

When two or more people work together, we simply add their daily work (or efficiency).

• If A does $\frac{1}{10}$ work per day, and B does $\frac{1}{15}$ work per day, their combined daily work is $\frac{1}{10}+\frac{1}{15}$.
• We usually use the LCM method (Total Work Units) because it avoids fractions and is faster for ssc gd time and work.

Formula for Combined Work (using LCM): $$\text{Time Taken}=\frac{\text{Total Work Units}}{\text{Total Daily Efficiency}}$$

These types of ssc gd time and work questions pdf in english are very common in the exam.

Solved Examples

Example 1: Two People Working Together

A can finish a task in 6 days and B can finish the same task in 12 days. If they work together, how many days will they take?

Solution:

1. First, find the Total Work (LCM): LCM of 6 and 12 is 12. (Total Work = 12 units).
2. Calculate Daily Efficiency:
   • A’s efficiency: $\frac{12}{6}=2$ units/day.
   • B’s efficiency: $\frac{12}{12}=1$ unit/day.
3. Calculate Combined Daily Efficiency: A + B $=2+1=3$ units/day.
4. Find the Time Taken: $$\text{Time}=\frac{\text{Total Work}}{\text{Combined Efficiency}}=\frac{12}{3}=4\text{ days}$$
5. So, the answer is: 4 days.

Example 2: Three People Working Together

P, Q, and R can finish a job in 10, 12, and 15 days, respectively. How long will they take if they all work together?

Solution:

1. First, find the Total Work (LCM): LCM of 10, 12, and 15 is 60. (Total Work = 60 units).
2. Calculate Daily Efficiency:
   • P: $\frac{60}{10}=6$ units/day.
   • Q: $\frac{60}{12}=5$ units/day.
   • R: $\frac{60}{15}=4$ units/day.
3. Calculate Combined Daily Efficiency: P + Q + R $=6+5+4=15$ units/day.
4. Find the Time Taken: $$\text{Time}=\frac{60}{15}=4\text{ days}$$
5. So, the answer is: 4 days. These ssc gd time and work questions require fast LCM calculation.

Example 3: One Person Leaves

A and B together can finish a job in 12 days. A alone can finish it in 20 days. How long will B alone take?

Solution:

1. First, find the Total Work (LCM): LCM of 12 (A+B) and 20 (A) is 60. (Total Work = 60 units).
2. Calculate Daily Efficiency:
   • (A + B)’s efficiency: $\frac{60}{12}=5$ units/day.
   • A’s efficiency: $\frac{60}{20}=3$ units/day.
3. Find B’s Daily Efficiency: We know A + B = 5 units, and A = 3 units. $$\text{B’s Efficiency}=(A+B)-A=5-3=2\text{ units/day}$$
4. Find B’s Total Time: $$\text{B’s Time}=\frac{\text{Total Work}}{\text{B’s Efficiency}}=\frac{60}{2}=30\text{ days}$$
5. So, the answer is: B takes 30 days.

Example 4: Working for a Few Days

Ram takes 10 days to complete a job. He works for 4 days and then leaves. How much work is left?

Solution:

1. First, find Ram’s Daily Work: Ram takes 10 days, so his daily work is $\frac{1}{10}$.
2. Calculate Work Done in 4 Days: $$\text{Work Done}=\text{Daily Work}\times \text{Days Worked}=\frac{1}{10}\times 4=\frac{4}{10}$$
3. Simplify the Work Done: $\frac{4}{10}=\frac{2}{5}$. Ram finished $\frac{2}{5}$ of the job.
4. Calculate Work Left: Total work is 1 (or $\frac{5}{5}$). $$\text{Work Left}=1-\frac{2}{5}=\frac{5}{5}-\frac{2}{5}=\frac{3}{5}$$
5. So, the answer is: $\frac{3}{5}$ of the work is left. These are key time and work ssc gd questions.

---

Finding the Time Taken (The Unitary Method)

Men, Days, and Work

Sometimes, ssc gd time and work problems involve changing the number of people (Men) or the hours they work.

• More Men = Less Time. (Inverse relationship)
• More Work = More Time. (Direct relationship)

We use the combined formula for these ssc gd time and work questions pdf:

$$\frac{M_1\times D_1\times H_1}{W_1}=\frac{M_2\times D_2\times H_2}{W_2}$$

Where:

• $M$ = Men (or workers)
• $D$ = Days
• $H$ = Hours per day
• $W$ = Work done (or units of work)

Solved Examples

Example 1: Men and Days

15 workers can build a road in 40 days. If 5 more workers join them, how many days will it take to build the same road?

Solution:

1. First, identify the knowns (Group 1): $M_1=15$, $D_1=40$. $W_1$ is the road (let $W_1=1$).
2. Identify the unknowns (Group 2): 5 more workers join, so $M_2=15+5=20$. $D_2=?$
3. Write down the formula (since work is the same, we ignore W): $M_1\times D_1=M_2\times D_2$
4. Put the numbers in: $$15\times 40=20\times D_2$$
5. Calculate $D_2$: $$D_2=\frac{15\times 40}{20}=\frac{600}{20}=30\text{ days}$$
6. So, the answer is: 30 days.

Example 2: Men, Days, and Hours

8 men working 9 hours a day can finish a task in 20 days. How many days will 12 men working 6 hours a day take to finish the same task?

Solution:

1. First, identify the knowns (Group 1): $M_1=8$, $H_1=9$, $D_1=20$.
2. Identify the unknowns (Group 2): $M_2=12$, $H_2=6$, $D_2=?$
3. Write down the formula: $M_1{D}_1{H}_1=M_2{D}_2{H}_2$
4. Put the numbers in: $$8\times 20\times 9=12\times D_2\times 6$$ $$1440=72\times D_2$$
5. Calculate $D_2$: $$D_2=\frac{1440}{72}=20\text{ days}$$
6. So, the answer is: 20 days.

Example 3: Men and Different Work

10 people can make 50 chairs in 5 days. How many chairs can 5 people make in 10 days?

Solution:

1. First, identify the knowns (Group 1): $M_1=10$, $D_1=5$, $W_1=50$.
2. Identify the unknowns (Group 2): $M_2=5$, $D_2=10$, $W_2=?$
3. Write down the formula: $\frac{M_1{D}_1}{W_1}=\frac{M_2{D}_2}{W_2}$
4. Put the numbers in: $$\frac{10\times 5}{50}=\frac{5\times 10}{W_2}$$ $$\frac{50}{50}=\frac{50}{W_2}$$
5. Calculate $W_2$: $$1=\frac{50}{W_2}$$ $$W_2=50$$
6. So, the answer is: They can make 50 chairs. These are important ssc gd time and work questions pdf in english.

Example 4: Efficiency Change

A group of workers was hired to finish a project in 40 days. If 5 workers had not shown up, the work would have taken 50 days. How many workers were originally hired?

Solution:

1. First, define variables: Let the original number of workers be $M_1=x$. $D_1=40$.
2. Define the second group: 5 workers did not show up, so $M_2=x-5$. $D_2=50$.
3. Set up the equation: $M_1\times D_1=M_2\times D_2$ $$x\times 40=(x-5)\times 50$$
4. Solve for x: $$40x=50x-250$$ $$250=50x-40x$$ $$250=10x$$
5. Calculate x: $$x=\frac{250}{10}=25$$
6. So, the answer is: 25 workers were originally hired.

---

Pipes and Cisterns (Tanks and Taps)

The Concept of Taps

Pipes and Cisterns is just another way to ask ssc gd time and work questions.

• Inlet Pipe (Filling): This is like a person doing positive work (adding water).
• Outlet Pipe (Emptying/Leak): This is like a person doing negative work (taking water away).

We use the same LCM method, but we subtract the efficiency of the outlet pipes.

Key Idea: If a pipe fills a tank in $T$ hours, its hourly work is $\frac{1}{T}$. If it empties, its hourly work is $-\frac{1}{T}$.

Solved Examples

Example 1: Two Inlet Pipes

Pipe A can fill a tank in 10 hours, and Pipe B can fill it in 15 hours. If both pipes are opened together, how long will it take to fill the tank?

Solution:

1. First, find the Total Capacity (LCM): LCM of 10 and 15 is 30. (Total Tank Capacity = 30 units).
2. Calculate Hourly Efficiency (Flow Rate):
   • A’s rate (filling): $\frac{30}{10}=+3$ units/hour.
   • B’s rate (filling): $\frac{30}{15}=+2$ units/hour.
3. Calculate Combined Rate: A + B $=3+2=5$ units/hour.
4. Find the Time Taken: $$\text{Time}=\frac{\text{Total Capacity}}{\text{Combined Rate}}=\frac{30}{5}=6\text{ hours}$$
5. So, the answer is: 6 hours.

Example 2: Inlet and Outlet Pipe

Pipe P can fill a tank in 20 minutes. Pipe Q can empty the same tank in 30 minutes. If both are open, how long will it take to fill the tank?

Solution:

1. First, find the Total Capacity (LCM): LCM of 20 and 30 is 60. (Total Capacity = 60 units).
2. Calculate Hourly Efficiency (Flow Rate):
   • P’s rate (filling): $\frac{60}{20}=+3$ units/minute.
   • Q’s rate (emptying): $\frac{60}{30}=-2$ units/minute. (It is negative because it removes water).
3. Calculate Combined Rate: P + Q $=3-2=1$ unit/minute.
4. Find the Time Taken: $$\text{Time}=\frac{60}{1}=60\text{ minutes}$$
5. So, the answer is: 60 minutes (or 1 hour). These are typical time and work ssc gd questions.

Example 3: Three Pipes Working Together

Tap X fills a tank in 6 hours, Tap Y fills it in 8 hours, and Tap Z empties it in 4 hours. If all three are opened, how long will it take to fill the tank?

Solution:

1. First, find the Total Capacity (LCM): LCM of 6, 8, and 4 is 24. (Total Capacity = 24 units).
2. Calculate Hourly Efficiency:
   • X (Inlet): $\frac{24}{6}=+4$ units/hour.
   • Y (Inlet): $\frac{24}{8}=+3$ units/hour.
   • Z (Outlet): $\frac{24}{4}=-6$ units/hour.
3. Calculate Combined Rate: X + Y + Z $=4+3-6=1$ unit/hour.
4. Find the Time Taken: $$\text{Time}=\frac{24}{1}=24\text{ hours}$$
5. So, the answer is: 24 hours.

Example 4: Filling Half the Tank

Pipe A fills a tank in 10 hours. After the tank is half full, Pipe B (which fills the tank in 5 hours) is also opened. How much total time is taken to fill the tank?

Solution:

1. First, find the Total Capacity (LCM): LCM of 10 and 5 is 10. (Total Capacity = 10 units).
2. Calculate Efficiency:
   • A’s rate: $\frac{10}{10}=1$ unit/hour.
   • B’s rate: $\frac{10}{5}=2$ units/hour.
3. Calculate Time for First Half: Half the tank is 5 units. Only Pipe A works. $$\text{Time 1}=\frac{5\text{ units}}{1\text{ unit/hour}}=5\text{ hours}$$
4. Calculate Time for Second Half: The remaining work is 5 units. Now A and B work together.
   • Combined Rate (A+B): $1+2=3$ units/hour. $$\text{Time 2}=\frac{5\text{ units}}{3\text{ units/hour}}=1.67\text{ hours (approx)}$$
5. Calculate Total Time: $$\text{Total Time}=\text{Time 1}+\text{Time 2}=5+1.67=6.67\text{ hours}$$
6. So, the answer is: 6.67 hours. Mastering these ssc gd time and work questions pdf will help you score high.