Correct Answer - Option 3 : 15/7 days
Given:
Time to complete the whole work by Arun and Bijay together = 3 days
Time to complete the whole work by Bijay and Chandan together = 5 days
Time to complete the whole work by Arun, Bijay and Chandan together = 2 days
Formula used:
Efficiency = Work Done/Time taken
Calculations:
Let the total work be LCM of 3, 5, 2 i.e. 30 units.
Let efficiency of Arun, Bijay and Chandan be A, B and C respectively.
Efficiency of A and B together,
⇒ A + B = 30/3 = 10 units/day ----(i)
Efficiency of Bijay and Chandan together,
⇒ B + C = 30/5 = 6 units/day ----(ii)
Efficiency of Arun, Bijay and Chandan together,
⇒ A + B + C = 30/2 = 15 units/day ----(iii)
⇒ 10 + C = 15
⇒ C = 5 units/day
B + C = 30/5 = 6 units/day
⇒ B = 6 - 5 = 1 unit/day
A + B = 30/3 = 10 units/day
⇒ A = 10 - 1 = 9 units/day
Efficiency of Arun and Chandan together,
⇒ A + C = 9 + 5
⇒ A + C = 14 units/day
Time taken by Arun and Chandan = 30/14
⇒ 15/7 days
∴ Arun & Chandan together will do it in 15/7 days.