Manjeet can complete a certain piece of work in 18 hours. Jaya is 100 percent more efficient than Manjeet, which means Jaya can work at twice Manjeet's rate. If both of them work together on this task, in how many hours will they finish the work?

Introduction / Context:

This time and work question focuses on using relative efficiency information to determine combined work rates. When one worker is stated to be 100 percent more efficient than another, it means that the more efficient worker can complete twice as much work in the same time. The problem then asks for the time taken when both work together, which is a common variation in work and efficiency questions.

Given Data / Assumptions:

• Manjeet alone can complete the work in 18 hours.
• Jaya is 100 percent more efficient than Manjeet, so Jaya's rate is twice Manjeet's rate.
• Both start together and work until the whole job is completed.
• We assume constant efficiency and take total work as one unit.

Concept / Approach:

The key idea is to first find Manjeet's work rate as a fraction of the job per hour, then use the relative efficiency information to express Jaya's rate as a multiple of Manjeet's rate. After that, we add their rates to get the combined rate for both working together. The time taken to complete the work is simply the total work divided by this combined rate, which corresponds to the reciprocal of the combined rate.

Step-by-Step Solution:

Verification / Alternative Check:

We can verify by checking how much work is done in 6 hours at the combined rate. In 6 hours, work completed = 6 * 1/6 = 1 unit of work, which is exactly the whole job. Also, Jaya alone at 1/9 per hour would finish the job in 9 hours, which is indeed faster than Manjeet's 18 hours and consistent with the statement that Jaya is twice as efficient as Manjeet.

Why Other Options Are Wrong:

A time of 3 hours would imply a combined rate of 1/3 per hour, which is higher than 1/18 + 1/9 and not supported by the given efficiencies. A time of 12 hours would imply a combined rate of 1/12 which is slower than even Jaya working alone. A time of 24 hours is clearly much slower and inconsistent, since Manjeet alone finishes in 18 hours. Only 6 hours matches the calculated combined rate of 1/6 per hour.

Common Pitfalls:

Some test takers misinterpret 100 percent more efficient as adding 100 percent of some other quantity incorrectly, or they treat it as meaning Jaya is only 1.5 times faster. The correct interpretation is that Jaya does 100 percent extra work compared with Manjeet, which means Jaya does twice as much in the same time. Another error is to average times instead of adding work rates, which leads to wrong answers.

Final Answer:

Working together, Manjeet and Jaya will finish the work in 6 hours.