Question

Four positive integers are given. If the average of any two of them is added to the remaining two integers, the numbers 46, 49, 48, 45, 44 and 47 are obtained. What is the average of the given four integers?
1. 15.5
2. 14.5
3. 14
4. 15

Answer 1

Correct Answer - Option 1 : 15.5

Let four numbers are P, Q, R, and S.

According to question:

Average of P and Q = (P + Q)/2

[(P + Q)/2] + R + S = 46  ------(1)

Average of P and R = (P + R)/2

[(P + R)/2] + Q + S = 49  ------(2)

Average of P and S = (P + S)/2

[(P + S)/2] + Q + R = 48  ------(3)

Average of Q and R = (Q + R)/2

[(Q + R)/2] + P + S = 45  ------(4)

Average of Q and S = (Q + S)/2

[(Q + S)/2] + P + R = 44  ------(5)

Average of R and S = (R + S)/2

[(R + S)/2] + P + Q = 47  ------(6)

Add all the equations;

(3 × P/2) + 3P + (3 × Q/2) + 3Q + (3 × R/2) + 3R + (3 × S/2) + 3S = (46 + 49 + 48 + 45 + 44 + 47)

9P/2 + 9Q/2 + 9R/2 + 9S/2 = 279

P + Q + R + S = 558/9

P + Q + R + S = 62

Average of P, Q, R, and S = 62/4 = 15.5

Hence, 15.5 is the correct answer.