Arun and Barun can do a piece of work in 72 days. Barun and Gitu can do it in 120 days.Arun and Gitu can do it in 90 days. In what time can Arun alone do it? 

Correct option is A

​Let the total work be LCM of 72, 120, and 90 = 720 units (for easier calculation).

Let’s define work rates:

• Arun + Barun do 720 units in 72 days → their combined rate = 720 ÷ 72 = 10 units/day

• Barun + Gitu do it in 120 days → rate = 720 ÷ 120 = 6 units/day

• Arun + Gitu do it in 90 days → rate = 720 ÷ 90 = 8 units/day

Now, add the first and third equations, then subtract the second:

• (Arun + Barun) + (Arun + Gitu) = 10 + 8 = 18

• Subtract (Barun + Gitu) = 6

So:
2Arun = 18 - 6 = 12 → Arun’s rate = 6 units/day

Now, total work = 720 units
Time = 720 ÷ 6 = 120 days

Answer: (A) 120 days