Raghav and Aditya can complete a work in 3 days. Aditya and Ishaan can complete the same work in 4 days. Ishaan and Raghav can complete it in 6 days. How many days will it take for Raghav, Aditya and Ishaan, combined together, to complete the same amount of work?

$2\frac{2}{3}$

Raghav(R) + Aditya(A) = 3 days,

Aditya(A) + Ishaan(I) = 4 days,

Ishaan(I) + Raghav(R) = 6 days,

⇒ Adding all the efficiencies = 2(Raghav + Aditya + Ishaan) = 9

⇒ (Raghav + Aditya + Ishaan) = \(\frac{9}{2}\)

⇒ Time required for Raghav + Aditya + Ishaan to complete the total work = \(\frac{12 × 2}{9}\) = \( { 2}_{ 3}^{ 2} \) days.      ..(\(\frac{Work}{Efficiency}\) = Time)