Three number are such that if the average of any two of them is added to the third number, the sums obtained are 186, 189 and 195 respectively. What is the average of the original three numbers ?

95

\(\frac{P +Q}{2}\) + R = 186,  

\(\frac{Q +R}{2}\) + P = 189

\(\frac{R +P}{2}\) + Q = 195

On adding all

⇒ \(\frac{2P + 2Q + 2R}{2}\) + (P+Q+R) = 570

⇒2 (P + Q + R) = 570

⇒ (P + Q + R) = 285

Avg of (P, Q & R) = \(\frac{P + Q + R}{3}\) = \(\frac{285}{3}\) = 95