Question

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?

• A. 13 47/121 days
• B. 10 25/31 days
• C. 11 19/78 days
• D. 12 23/103 days

Answer 1

Answer:

A. 13 47/121 days

Let total work = 1

Individual work rates:

• Ravi: $( \frac{1}{4} )$ work in 15 days
  ⇒ 1 day work = $( \frac{1}{4 \times 15} = \frac{1}{60} )$

• Chavi: $( \frac{1}{3} )$ work in 18 days
  ⇒ 1 day work = $( \frac{1}{54} )$

• Dhani: $( \frac{1}{2} )$ work in 24 days
  ⇒ 1 day work = $( \frac{1}{48} )$

  Total work per day:

• $\frac{1}{60} + \frac{1}{54} + \frac{1}{48}$
  

LCM = 2160

$= \frac{36 + 40 + 45}{2160} = \frac{121}{2160}$

Time to complete ( \frac{3}{4} ) work:

• $\text{Time} = \frac{3/4}{121/2160}$
  $= \frac{3}{4} \times \frac{2160}{121}$

  
  $= \frac{1620}{121}$

  
  $\approx 13 \frac{47}{121} \text{ days}$