The average weight of P and his three friends is 55 kg. If P is 4 kg more than the average weight of his three friends, what is P's weight (in kg)?

Question: The average weight of P and his three friends is 55 kg. If P is 4 kg more than the average weight of his three friends, what is P's weight (in kg)?

Solution:
Average weight of P and his 3 friends = 55 kg
P's weight is 4 kg more than the average weight of his 3 friends.

Let the average weight of the 3 friends be x kg.
∴ Total weight of the 3 friends = 3x kg
And weight of P = (x + 4) kg

∴ Total weight of all 4 persons = 4 × 55 = 220 kg

ATQ,
3x + (x + 4) = 220
⇒ 4x + 4 = 220
⇒ 4x = 220 - 4 = 216
⇒ x = 216/4
∴ x = 54 kg

∴ P's weight = x + 4 = 54 + 4 = 58 kg

Shortcut Trick
Total weight of P and his 3 friends = 4 × 55 = 220 kg.
Let P's weight be P. The average of the 3 friends is (P − 4) kg.

Total weight = P + 3 × (P - 4) = 220
⇒ 4P - 12 = 220
⇒ 4P = 232
⇒ P = 232/4 = 58 kg.