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A is thrice as efficient as B and B is twice as efficient as C. If A, B and C work together how long will they take to complete a job which B completes in 10 days?

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\frac{20}{9} days

\frac{11}{9} days

3 days

None of these

answer is A.

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Detailed Solution

Given, time taken to B to complete work = 10 days.
As A is 3 times efficient than B. Thus, time taken to A to complete work
=

\frac{10}{3}

days.
Now b is twice efficient than C. Thus, time taken to C to complete work
=

2 \times 10

= 20

days
Now, one day work of A, B and C (working together),

= \frac{3}{10} + \frac{1}{10} + \frac{1}{20}

= \frac{6 + 2 + 1}{20}

= \frac{9}{20}

Therefore, number of days required to finish work when all three work together,

= \frac{1}{one day work of A + B + C}

= \frac{1}{\frac{20}{9}}

= \frac{20}{9}

days
Option 1 is correct.

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