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, and Rachel is 50% as efficient as Rahim. In how many more days will they complete the work?

• A. 121/3
• B. 51/7
• C. 40/7
• D. 65/7

Hint:

Ram’s daily rate is 4% of the job; the combined rate of all three is 7% of the job per day, and 40% remains.

Answer 1

The Correct Option is C

It helps to express every rate as a simple fraction of Ram's rate from the start, avoiding decimals.

1. Ram's rate: 1 unit (of Ram's own daily output).
2. Rahim's rate: half of Ram's, so $\frac{1}{2}$.
3. Rachel's rate: half of Rahim's, so $\frac{1}{4}$.
4. Combined daily rate $= 1 + \frac{1}{2} + \frac{1}{4} = \frac{7}{4}$ (in units of Ram's daily rate).
5. Since Ram finishes 60% of the job in 15 days, his daily rate is $\frac{60\%}{15} = 4\%$ of the job per day, and 40% of the job remains.
6. Days needed by all three together $= \dfrac{40\%}{\frac{7}{4}\times 4\%} = \dfrac{40\%}{7\%} = \dfrac{40}{7}$ days.

So the correct answer is option C, 40/7 days.