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

Step 1: Set up the total work.
Ram completes 60% of the task in 15 days, so let the total work be 25x units (so that 60% of 25x, which is 15x, is done in 15 days), giving Ram's rate as x units per day.

Step 2: Find Rahim's and Rachel's rates.
Rahim is 50% as efficient as Ram: rate \(=0.5x\). Rachel is 50% as efficient as Rahim: rate \(=0.25x\).

Step 3: Find the remaining work.
Ram has completed \(15x\) units (60% of 25x), so the remaining work is \(25x-15x=10x\) units.

Step 4: Find the combined rate and time.
Combined rate of all three \(=x+0.5x+0.25x=1.75x\) per day. Time \(=\dfrac{10x}{1.75x}=\dfrac{10}{1.75}=\dfrac{1000}{175}=\dfrac{40}{7}\) days.

Step 5: Final Answer.
They take \(\dfrac{40}{7}\) more days, so option C is correct.