Correct Answer - Option 4 : 6 days

**Given:**

P = 2Q

Q = 3R

R can complete a work in 54 days

**Concept used:**

If A does a work in n days then 1-day work of A is 1/n

**Calculation:**

According to question

Let, P's one day work = 6 unit

⇒ Q's one day work = 3 unit

⇒ R's one day work = 1 unit

R can complete work in 54 days

⇒ Total work = 1 × 54 = 54 unit

⇒ (P + Q) can complete work in = 54/( 6 + 3)

⇒ 54/9

⇒ 6 days

**∴ P and Q together can complete work in 6 days**