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A, B and C complete a task in 8 days. A or B alone can complete the same task in 20 days. In how many days can C alone complete the same task?
Question

A, B and C complete a task in 8 days. A or B alone can complete the same task in 20 days. In how many days can C alone complete the same task?

A.

35

B.

30

C.

40

D.

45

Correct option is C

Given:

A, B, and C together complete the work in 8 days

A alone = 20 days

B alone = 20 days

Find time taken by C alone

Concept Used:
Work rate =1Time \frac{1}{\text{Time}}​​

Solution:

Work = 1 unit (assumed total work)

Total work rate=18=\frac{1}{8} ​​

A's rate =120,=\frac{1}{20},​​

B's rate =120 \frac{1}{20}

1C=18(120+120)\frac{1}{C} = \frac{1}{8} - \left(\frac{1}{20} + \frac{1}{20}\right)​​

1C=18220=18110=5440=140\frac{1}{C} = \frac{1}{8} - \frac{2}{20} = \frac{1}{8} - \frac{1}{10} = \frac{5 - 4}{40} = \frac{1}{40}​​

C alone can do the work in 40 days

Alternate Method:

Efficiency of C = 5 - 2 - 2 =1 

Time taken by C = 401=40\frac {40}1 =40 days​

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