Correct option is D
Given
Mahi takes twice the time of (Neha + Asha)
Asha takes three times the time of (Neha + Mahi)
Total time taken by all three working together = 20 days
Formula Used
Efficiency is inversely proportional to time.
Total Work = Total Efficiency Time
Solution
From the time ratios, we can determine the efficiency ratios.
Mahi's efficiency to (Neha + Asha)'s efficiency = 1 : 2
Total efficiency in this case is 1 + 2 = 3 units.
Asha's efficiency to (Neha + Mahi)'s efficiency = 1 : 3
Total efficiency in this case is 1 + 3 = 4 units.
To make the total efficiency equal for both scenarios, take the LCM of 3 and 4, which is 12.
Multiply the first ratio by 4: Mahi's efficiency = 4 units.
Multiply the second ratio by 3: Asha's efficiency = 3 units.
Total efficiency of all three = 12 units.
Neha's efficiency = Total - (Mahi + Asha)
Neha's efficiency = 12 - (4 + 3) = 5 units.
Total Work = units.
Time taken by Neha alone = days
Final Answer
So the correct answer is (d)