Solve Time & Work Problems in Under 30 Seconds

Time and Work problems are a crucial part of competitive exams and placement tests. While these questions can seem complex, applying the right shortcut techniques can help you solve them in seconds.

This guide will introduce a fast and efficient method to solve Time and Work problems without lengthy calculations.

Shortcut Approach to Solve Time and Work Problems

Time and Work problems revolve around three key elements:

• Total Work – The entire task to be completed
• Efficiency – Work done per unit of time
• Time Taken – The total duration required to complete the work

Instead of using traditional methods, the LCM method simplifies calculations significantly.

Key Formulas

1. Total Work = LCM of given time values
2. Efficiency = Total Work ÷ Time Taken
3. Time Taken = Total Work ÷ Total Efficiency

Using this approach, solving problems involving multiple workers becomes quick and easy.

Example 1: Two People Working Together

Question:

A can complete a task in 12 days, and B can complete the same task in 18 days. How long will it take for them to complete the work together?

Solution Using the Shortcut Method

1. Find LCM of 12 and 18
   • LCM(12,18) = 36 (Consider this as the total work)
2. Calculate Efficiency
   • A’s efficiency = 36 ÷ 12 = 3 units/day
   • B’s efficiency = 36 ÷ 18 = 2 units/day
   • Total efficiency = 3 + 2 = 5 units/day
3. Calculate Total Time
   • Total Work ÷ Efficiency = 36 ÷ 5 = 7.2 days

Final Answer: 7.2 days or 7 days and approximately 5 hours

This approach significantly reduces the time required to solve the question compared to traditional methods.

Example 2: Three People Working Together

Question:

A can complete a task in 15 days, B in 10 days, and C in 30 days. How long will it take if they work together?

Solution Using the Shortcut Method

1. Find LCM of 15, 10, and 30
   • LCM(15,10,30) = 30 (Consider this as the total work)
2. Calculate Efficiency
   • A’s efficiency = 30 ÷ 15 = 2
   • B’s efficiency = 30 ÷ 10 = 3
   • C’s efficiency = 30 ÷ 30 = 1
   • Total efficiency = 2 + 3 + 1 = 6 units/day
3. Calculate Total Time
   • Total Work ÷ Efficiency = 30 ÷ 6 = 5 days

Final Answer: 5 days

Using this method, multiple worker problems can be solved in seconds.

Special Cases and Tricks

1. If a Person Leaves Midway

If one person stops working after a few days, adjust the calculation by:Work done before leaving+Remaining work=Total Work\text{Work done before leaving} + \text{Remaining work} = \text{Total Work}Work done before leaving+Remaining work=Total Work

Then use the efficiency formula to determine the remaining time.

2. If Work Increases or Decreases

If the total work doubles, the time required also doubles. If efficiency doubles, time is halved. Use these proportional relationships to quickly adjust your calculations.

Practice Questions

Try solving these problems using the shortcut method:

1. A can complete a task in 20 days, and B in 30 days. How long will they take to complete it together?
2. A, B, and C can complete a work in 12, 24, and 36 days respectively. How long will they take together?
3. A can do a job in 10 days but leaves after 5 days. B alone finishes the remaining work in 5 days. How long would B alone take to complete the full work?

Check your answers using the efficiency shortcut and compare your solving time with traditional methods.

Final Thoughts

Mastering Time and Work shortcuts can help in exams like CAT, SSC, Bank PO, and placement tests. By practicing these techniques, you can improve both speed and accuracy.