# The average height of P, Q and R is 150 cms. If the average height of P and Q is 150 cms and the average height of Q and R is 155 cms then, what is th

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The average height of P, Q and R is 150 cms. If the average height of P and Q is 150 cms and the average height of Q and R is 155 cms then, what is the height of Q?

1. 155 cms
2. 150 cms
3. 160 cms
4. 170 cms

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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.