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Mahi would need twice as much time as Neha and Asha combined, while Asha would require three times as much time as Neha and Mahi combined to complete
Question

Mahi would need twice as much time as Neha and Asha combined, while Asha would require three times as much time as Neha and Mahi combined to complete a certain task. If all three friends work together, they can finish the task in 20 days. How many days would Neha take to complete the same task on her own?

A.

42 days

B.

24 days

C.

36 days

D.

48 days

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 ×\times​ 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 = 12×20=24012 \times 20 = 240​ units.
Time taken by Neha alone = 2405=48 \frac{240}{5} = 48 \; ​days
Final Answer
So the correct answer is (d)

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