Three number are such that if the average of any two of them is added to the third number, the sums obtained are 56, 59 and 65 respectively. What is the average of the original three numbers ?

30

Let three numbers are P , Q &  R . 

According to question ,

\(\frac{P +Q}{2}\) + R = 56,  

\(\frac{Q +R}{2}\) + P = 59

\(\frac{R +P}{2}\) + Q = 65

On adding all

\(\frac{2P + 2Q + 2R}{2}\) + (P+Q+R) = 180

2 (P + Q + R) = 180

(P + Q + R) = 90

Average of (P, Q & R) = \(\frac{P + Q + R}{3}\) = \(\frac{90}{3}\) = 30