Question

Ram completes 60% of a task in 15 days and then takes the help of Rahim and Rachel. Rahim is 50% as efficient as Ram is and Rachel is 50% as efficient as Rahim is. In how many more days will they complete the work?

• A. \(121\\\,\,\,\,3\)
• B. \(51\\7\)
• C. \(40\\7\)
• D. \(65\\7\)

Answer 1

The Correct Option is C

To solve this problem, we need to determine the total number of days required to complete the task when Ram is assisted by Rahim and Rachel. We first need to understand the individual efficiencies and from there deduce the collective efficiency. 

1. First, calculate the total work required. Since Ram completes 60% of the task in 15 days, the entire task represents a total of 15/0.6 days of his work, which is \(25\) days of work for Ram.
2. Ram's efficiency is \(\frac{1}{25}\) of the task per day.
3. Rahim is 50% as efficient as Ram, so his efficiency is \(\frac{1}{50}\) of the task per day.
4. Rachel is 50% as efficient as Rahim, so her efficiency is \(\frac{1}{100}\) of the task per day.
5. Combined, their daily efficiency is:

\(\frac{1}{25} + \frac{1}{50} + \frac{1}{100} = \frac{4 + 2 + 1}{100} = \frac{7}{100}\)

1. Ram has already completed 60% of the work, thus 40% remains.

Work left = \(\frac{2}{5}\) of the task.

1. The number of days to complete the remaining task with the combined efficiency is:

\(\frac{\frac{2}{5}}{\frac{7}{100}} = \frac{2}{5} \times \frac{100}{7} = \frac{200}{35} = \frac{40}{7}\)

Therefore, with Ram, Rahim, and Rachel working together, the task will be completed in \(\frac{40}{7}\) more days.