Mayur can complete a piece of work in 27 hours. If he is joined by Jayantika, who is 100 percent more efficient than him, in how many hours will they finish the work together?

Introduction / Context:
This is a classic work and time problem that appears frequently in quantitative aptitude tests. It checks your understanding of the relationship between time taken to complete a job and individual efficiency, and how combined efficiency affects the total time when two people work together on the same task.

Given Data / Assumptions:

• Mayur completes the work alone in 27 hours.
• Jayantika is 100 percent more efficient than Mayur, meaning she is twice as efficient.
• Both work together on the same task from start to finish.
• Work rate is assumed constant for each person.

Concept / Approach:
Efficiency is inversely proportional to time taken for the same work. If a person is 100 percent more efficient, his or her work rate doubles. We convert times into rates of work, sum the rates, and then invert the combined rate to find the total time:

• Work rate = 1 / time
• Total rate when working together is the sum of individual rates.

Step-by-Step Solution:
Mayur time = 27 hours, so Mayur rate = 1 / 27 of the work per hour Jayantika is 100 percent more efficient, so her rate is 2 times Mayur rate Jayantika rate = 2 * (1 / 27) = 2 / 27 of the work per hour Combined rate = 1/27 + 2/27 = 3/27 = 1/9 of the work per hour If they complete 1 full work at a rate of 1/9 per hour, total time = 1 / (1/9) = 9 hours

Verification / Alternative check:
Think of the total work as 27 units. Mayur alone completes 1 unit per hour. Since Jayantika is twice as efficient, she completes 2 units per hour. Together they complete 3 units per hour. To complete 27 units, time required is 27 / 3 = 9 hours, which matches the previous calculation.

Why Other Options Are Wrong:
If the answer were 6 hours, the combined rate would have to be 1/6, which is too high compared to the calculated 1/9. Options 3 hours and 10 hours also do not match the computed work rate. Eighteen hours is closer to Mayur time and would imply very low extra efficiency, contradicting the 100 percent more efficient statement.

Common Pitfalls:
A frequent misunderstanding is to think that 100 percent more efficient means taking half the time without relating it to work rate. Another common mistake is to average the times directly rather than adding the rates. Always convert times to rates, sum the rates, and then invert to obtain the final time.

Final Answer:
Working together, Mayur and Jayantika will finish the work in 9 hours.