Question

The average height of two men P and Q is 167 cm. Another man R Joins them and the average height of P, Q and R become 162 cm. If another man S whose height is 17 cm more than that of R replaces P, then the average height of Q, R and S become 157 cm. What is the height of P?
1. 180 cm
2. 182 cm
3. 184 cm
4. 183 cm

Answer 1

Correct Answer - Option 3 : 184 cm

Given:

The average height of men P and Q = 167 cm

The average height of the men P, Q, and R = 162 cm

Concept:

\(Average\ =\ {The\ sum\ of\ all\ items \over The\ total\ numbe\ of\ items}\)

Calculation:

Let us assume the height of the P be X

⇒ P + Q = 167 × 2 = 334     ----(1)

⇒ P + Q + R = 162 × 3 = 486     ----(2)

⇒ The height of the R = 486 - 334 = 152 cm

⇒ The height of the S = 152 + 17 = 169 cm

⇒ Q + R + S = 157 × 3 = 471     ----(3)

⇒ The height of the Q = 471 - 152 - 169 = 471 - 321 = 150 cm

⇒ The height of the P = X = 334 - 150 = 184 cm

∴ The required result will be 184 cm.