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**