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Ravi, Arvind and Vimal can complete a piece of work in 5 days, 6 days and 8 days, respectively. In how many days can all the three together compl
Question

Ravi, Arvind and Vimal can complete a piece of work in 5 days, 6 days and 8 days, respectively. In how many days can all the three together complete the work?

A.

3451 days 3 \dfrac{4}{51} \text{ days} \quad

B.

2259 days2 \dfrac{2}{59} \text{ days} \quad​​

C.

3665 days3 \dfrac{6}{65} \text{ days} \quad​​

D.

2347 days2 \dfrac{3}{47} \text{ days}​​

Correct option is B

Given:

Ravi completes work in 5 days

Arvind completes work in 6 days

Vimal completes work in 8 days

Solution:

Ravi completes work in 5 days 

Work rate = 15\frac 15​ per day

Arvind completes work in 6 days 

Work rate = 16\frac 16​ per day

Vimal completes work in 8 days

Work rate = 18\frac 18 per day

Total work rate = 15+16+18\frac 15 + \frac16 + \frac18​​

= 24+20+15120\frac {24+20+15}{120}​​

=59120\frac {59}{120}​ work per day

Time = 159120\frac{1}{\frac{59}{120}}​= 12059\frac{120}{59} =22592 \dfrac{2}{59} days

Alternate Method:

Total work = 120 unit

Total efficiency = 24 + 20 + 15 = 59

Time = 12059\frac{120}{59} =22592 \dfrac{2}{59} days

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