Option 1 : 4 days

**Given**:

A can do in 12 days, B can do in 15 days and C is 20% more efficient then A

**Calculation:**

The ratio of efficiency of A and C = 5 : 6

Hence, the ratio of time taken to do a work by A and C = 6 : 5

So,

If A can do work in 12 days

C will do the same work in 10 days

According to question,

A can do the work in 12 days

Thus A work at the ratio = 1/12

B can do the work in 15 days

Thus B work at the ratio = 1/15

C can do the work in 10 days

Thus C work at the ratio 1/10

Work together A, B and C

⇒ [(1/12) + (1/10) + (1/15)]

⇒ 15/60 = 1/4

**∴ Together we can complete the work in 4 days **

**Short trick:**

If A, B and C can do a work in x, y and z days respectively then all of them working together can finish the work in{ \(\frac{{xyz}}{{xy + yz + zx}}\)} days

The ratio of efficiency of A and C = 5 : 6

Hence, the ratio of time taken to do a work by A and C = 6 : 5

C will do the same work in 10 days, A = 12 days and B = 15 days

⇒ [(10× 12 × 15)/ (120 + 180 + 150)]

⇒ 4 days

∴ Together we can complete the work in 4 days