Ameesha can complete a task by herself in 14 days, while it takes Bhavya 35 days to complete it alone. Together with Chitra, they can complete the task in 6 days. How many days will Chitra need to complete the task alone?

Correct option is D

Given:
Ameesha completes the task in 14 days.
Bhavya completes the task in 35 days.
All three (Ameesha + Bhavya  +  Chitra) together complete the task in 6 days.
Concept Used:
Work and time problems are solved using the concept of efficiency or work per day.
If a person completes a work in D days, then their one day work is $$\frac 1D$$​.
Formula Used:
​$$\text{One day work} = \frac{1}{\text{Total days to complete the work}} \\\text{Chitra's one day work} = \left( \text{One day work of all three} \right) - \left( \text{Ameesha's one day work} + \text{Bhavya's one day work} \right)$$​​
Solution:
Ameesha's one day work = $$\frac {1}{14}$$​​
Bhavya's one day work = $$\frac {1}{35}$$​
Together (Ameesha + Bhavya + Chitra), one day work = $$\frac {1}{6}$$​
Ameesha and Bhavya's work together in one day =  $$\frac{1}{14} + \frac{1}{35} = \frac{5 + 2}{70} = \frac{7}{70} = \frac{1}{10} \\$$​

Chitra's one day work $$= \frac{1}{6} - \frac{1}{10} = \frac{5 - 3}{30} = \frac{2}{30} = \frac{1}{15}$$​
So, Chitra alone can complete the task in 15 days.
Alternate Solution:
Total work = LCM of 14, 35, and 6 = 210 units
Ameesha's 1 day work = 210 ÷ 14 = 15 units/day
Bhavya's 1 day work = 210 ÷ 35 = 6 units/day
Ameesha + Bhavya + Chitra's 1 day work = 210 ÷ 6 = 35 units/day
Chitra's 1 day work = 35 - (15 + 6) = 35 - 21 = 14 units/day
Time taken by Chitra to complete 210 units alone = 210 ÷ 14 = 15 days