Question

The average height of 3 men P, Q, and R is 180 cm. Another man S joins the group and the average now becomes 170 cm. If another man T, whose height is 5 cm more than that of S, replaces P, then the average height of Q, R, S, and T becomes 168 cm. The height of P is:

1. 140 cm
2. 153 cm
3. 166 cm
4. 150 cm
5. 186 cm

Answer 1

Correct Answer - Option 2 : 153 cm

Calculation:

Let P, Q, R, S, and T represent their respective heights.

∴ P + Q + R = (180 × 3)

⇒ 540

∴ P + Q + R + S = (170 × 4)

⇒ 680

∴ S = 680 – 540

⇒ 140 cm

∴ T = 140 + 5

⇒ 145 cm

∴ Q + R + S + T = (168 × 4)

⇒ 672 cm

Now, (P + Q + R + S) – (Q + R + S + T)

⇒ 680 – 672

⇒ 8 cm

∴ P – T = 8

∴ P = T + 8

⇒ P = 145 + 8

⇒ P = 153 cm

The height of P is 153 cm.