Ravi can complete one-fourth of the total work in 15 days, Chavi can complete one-third of the total work in 18 days, Dhani can complete half of the total work in 24 days. In how much time can Ravi, Chavi and Dhani complete three-fourth of the work together?

Correct option is A

Given:

- Ravi completes $$\frac{ 1}{4}$$​ work in 15 days.

- Chavi completes $$\frac{ 1}{3 }$$​work in 18 days.

- Dhani completes $$\frac{1}{2}$$​ work in 24 days.

Formula Used:

- Total work = Part of work × Time taken

- Efficiency (Work per day) = $$\frac{1 }{ Total\ time\ taken}$$​​

- Total Time =  $$\frac{Total \ Work }{ Combined \ Efficiency}$$​​

- To find combined work rate:  $$\frac{1}{A} +\frac{ 1}{B} +\frac{ 1}{C}$$​​

Solution:

Ravi completes 1/4 work in 15 days => Total work = 4 × 15 = 60 days => Ravi's 1 day work =  $$\frac{1}{60}$$​​

Chavi completes 1/3 work in 18 days => Total work = 3 × 18 = 54 days => Chavi's 1 day work = $$\frac{1}{54}$$​​

Dhani completes 1/2 work in 24 days => Total work = 2 × 24 = 48 days => Dhani's 1 day work =  $$\frac{1}{48}$$​​

Combined 1 day work = $$\frac{1}{60} +\frac{ 1}{54} + \frac{1}{48}$$​​

LCM of 60, 54 and 48 = 2160

So, $$\frac{1}{60} + \frac{1}{54} + \frac{1}{48} = \frac{36 + 40 + 45}{2160} = \frac{121}{2160}$$​​

Work to be done = $$\frac{3}{4}$$​ of total work

Required Time = $$\left(\frac{3}{4}\right) \div \left(\frac{121}{2160}\right) = \left(\frac{3}{4}\right) \times \left(\frac{2160}{121}\right) = \frac{1620}{121}$$  = $$13\frac{47}{121}$$ days​

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