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.