Correct Answer - Option 1 :
14\(\frac{2}{3}\)
Given:
Time taken by A to do the job = 10 days
Time taken by B to do the job = 30 days
Formula used:
Total Work = Time Taken × Efficiency
⇒ Efficiency = Total Work/Time Taken
Calculation:
Let the total work be the LCM of 10 and 30 units
⇒ Total Work = 30
One day efficiency of A = 30/10 = 3 units
One day efficiency of B = 30/30 = 1 unit
Work done by A and B in 2 days working alternatively = (3 + 1) = 4
⇒ 2 × 7 days = 4 × 7
⇒ 14 days = 28 units
Now, A will do the remaining (30 - 28) 2 units in = 2/3 days
∴ The total time taken by A and B = (14 + 2/3)
⇒ 14\(\frac{2}{3}\) days