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There are three numbers. When the average of any two is added to the third number, the resulting numbers are 104, 111 and 115, What is the average of the given three numbers?

There are three numbers. When the average of any two is added to the third number, the resulting numbers are 104, 111 and 115, What is the average of the given three numbers? Correct Answer 55

Given:

Average of any two number + third number = 104

Average of any two number + third number = 111

Average of any two number + third number = 115

Formula used:

Average = Sum of observation/Total number of observation

Calculation:

Let the number be a, b and c

According to the question

(a + b)/2 + c =104

⇒ (a + b + 2c)/2 = 104

⇒ a + b + 2c = 208      ----(i)

(a + c)/2 + b =111

⇒ (a + c + 2b)/2 = 111

⇒ a + c + 2b = 222      ----(ii)

(b + c)/2 + a =115

⇒ (b + c + 2a)/2 = 115

⇒ b + c + 2a = 230      ----(iii)

After adding equation (i), (ii) and (iii) we get

4a + 4b + 4c = 208 + 222 + 230

⇒ a + b + c = 660/4

⇒ (a + b + c)/3 = 165/3

⇒ (a + b + c)/3 = 55

∴  The average of the three number is 55.

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