Correct Answer - Option 3 : 160 cms

**Given: **

The average height of P, Q, and R = 150 cms.

The average height of P and Q = 150 cms.

The average height of Q and R = 155 cms.

**Formula used:**

Average = (Sum of observation)/(Total number of observations)

**Calculation:**

Let the height of P, Q and R be P, Q and R respectively.

According to the question,

(P + Q + R)/3 = 150

⇒ P + Q + R = 3 × 150

⇒ P + Q + R = 450 ---(i)

and , (P + Q)/2 = 150

⇒ P + Q = 2 × 150

⇒ P + Q = 300 ---(ii)

and , (Q + R)/2 = 155

⇒ Q + R = 2 × 155

⇒ Q + R = 310 ---(iii)

Adding equation (ii) and (iii), we get

P + Q + Q + R = 300 + 310

⇒ P + 2Q + R = 610 ---(iv)

Subtracting equation (i) from equation (ii), we get

(P + 2Q + R) – (P + Q + R) = 610 – 450

⇒ 2Q – Q = 160

⇒ Q = 160 cms

**∴**** The height of Q is 160 cms.**