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 => full work in 60 days.

Chavi completes $$\frac{1}{3}$$​ work in 18 days => full work in 54 days.

Dhani completes $$\frac{1}{2}$$​ work in 24 days => full work in 48 days.

Formula Used:

Work = Rate × Time

Solution:

Let total work = 720 units

Ravi's rate = $$\frac{720}{60} = 12 \text{ units/day}$$​​

Chavi's rate = $$\frac{720}{54} = \frac{40}{3} \text{ units/day}$$​​

Dhani's rate = $$\frac{720}{48} = 15 \text{ units/day}$$​​

Combined rate = $$12 + \frac{40}{3} + 15$$​​

​$$= 27 + \frac{40}{3} \\ \ \\= \frac{81 + 40}{3} \\ \ \\ = \frac{121}{3} \text{ units/day}$$​​

Time for $$\frac{3}{4}$$​ work  = $$\frac{\frac{3}{4} \times 720}{\frac{121}{3}}$$​​

​$$= \frac{540 \times 3}{121} \\ \ \\= \frac{1620}{121} \\ \ \\ = 13\frac{47}{121} \text{ days}$$​​