S can complete a task in 50 days, T can complete it in 40 days and M can complete it in 30 days. S can work on all days of the week; T can work only on Monday, Wednesday, and Friday while M can work only on Saturday and Sunday. The work is started on Monday. In how many weeks it will be completed?

Correct option is C

Given:

S completes the task in 50 days 

T completes the task in 40 days 

M completes the task in 30 days

Work pattern:

Work starts on Monday

S works every day

T works Monday, Wednesday, Friday

M works Saturday, Sunday

Solution:

S works 7 days → $$7 \times \frac{1}{50} = \frac{7}{50}$$​​

T works 3 days → $$3 \times \frac{1}{40} = \frac{3}{40}$$​​

M works 2 days → $$2 \times \frac{1}{30} = \frac{2}{30} = \frac{1}{15}$$

Total weekly work : 

​$$= \frac{7}{50} + \frac{3}{40} + \frac{1}{15}$$​​

​$$= \frac{84 + 45 + 40}{600} = \frac{169}{600}$$​​

Time = $$\frac{1}{\frac{169}{600}} = \frac{600}{169} \approx 3.55 \text{ weeks}$$​​

Thus, Work will be completed between 3 to 4 weeks.

Alternate Solution: