Sita and Gita can do a piece of work together in 12 days. If Gita is three times more efficient than
Sita, how long will Sita take to complete the work alone?
1. 16 days
2. 48 days
3. 24 days
4. 32 days

Work Efficiency of Sita and Gita – Detailed Explanation

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Introduction to Work Efficiency

In mathematical problems involving work and efficiency, understanding how different individuals contribute to completing a task helps in calculating the time required by each person to complete the work alone. When two or more individuals work together, their combined efficiency determines how quickly the work is completed.

In this article, we will solve a problem involving Sita and Gita’s work efficiency and determine how long Sita will take to complete the work alone.

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✅ Key Phrase: Work Efficiency of Sita and Gita

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✅ Question and Answer

Question:
Sita and Gita can do a piece of work together in 12 days. If Gita is three times more efficient than Sita, how long will Sita take to complete the work alone?

1. 16 days
2. 48 days
3. 24 days
4. 32 days

Correct Answer: ✔️ Option 2 – 48 days

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Explanation of the Problem

1. Define the Work Efficiency

Let:

• Sita’s work efficiency = x (amount of work done by Sita in one day)
• Gita’s work efficiency = 3x (because Gita is three times more efficient than Sita)

Therefore, the total work done by Sita and Gita together in one day =x+3x=4x

2. Use the Given Condition

Sita and Gita together complete the work in 12 days. Therefore, the total work is:

Total work    =     Efficiency×Number of days

4x×12=48x

3. Find Sita’s Time to Complete the Work Alone

If Sita works alone, the time she will take to complete the same amount of work =

Total Work Sita’s Efficiency= 48x/ x

                                                  =48 days

Correct Answer:

✔️ Sita will take 48 days to complete the work alone.

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4. Step-by-Step Calculation Recap

1. Sita’s efficiency = x
2. Gita’s efficiency = 3x
3. Combined efficiency = 4x
4. Total work = 4x × 12 = 48x
5. Time for Sita to complete the work alone =

48/ x=48 days

 

5. Why Efficiency Matters in Work Problems

• Work and efficiency problems help evaluate productivity and time management.
• By understanding the contribution of each worker, you can estimate the completion time under different working conditions.
• This concept applies in fields like project management, workforce planning, and operational research.

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✅ Efficiency Calculation Formula

The general formula for work and efficiency problems is:

Total Work=Efficiency×Time

If two workers A and B work together, the combined efficiency is:

Efficiency of A+   Efficiency of B

If they complete the work together in T days, the total work becomes:

(Efficiency of A+ Efficiency of B)×T

Significance of Work Efficiency in Competitive Exams

Questions on work efficiency frequently appear in competitive exams like:

• CSIR NET Life Science
• DBT BET JRF
• IIT JAM
• GATE Biotechnology

Understanding how to solve these problems quickly can give you a significant edge over other candidates.

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Comparison of Individual and Combined Work Efficiency

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Conclusion

The correct answer to the problem is 48 days. Sita and Gita’s combined efficiency allows them to complete the work faster, but when working individually, their respective efficiencies determine how long they will take to complete the task.

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