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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 o
Question

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?

A.

Between 4 to 5 weeks

B.

Exactly 3 weeks

C.

Between 3 to 4 weeks

D.

Between 2 to 3 weeks

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 → 7×150=7507 \times \frac{1}{50} = \frac{7}{50}​​

T works 3 days → 3×140=3403 \times \frac{1}{40} = \frac{3}{40}​​

M works 2 days → 2×130=230=1152 \times \frac{1}{30} = \frac{2}{30} = \frac{1}{15}

Total weekly work : 

=750+340+115= \frac{7}{50} + \frac{3}{40} + \frac{1}{15}​​

=84+45+40600=169600= \frac{84 + 45 + 40}{600} = \frac{169}{600}​​

Time = 1169600=6001693.55 weeks\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:

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