Three numbers are such that if the average of any two of them is added to the third number the sums ...........

Quantitative Aptitude (CGL) Average

Three numbers are such that if the average of any two of them is added to the third number, the sums obtained are 168, 174

and 180 respectively. What is the average of the original three numbers ?

This questions was previously asked in

SSC CGL 4 June 2019 Shift-3

- Let's denote the three numbers as \( a \), \( b \), and \( c \).

- The first condition states that \((a + b) / 2 + c = 168\).

- The second condition states that \((b + c) / 2 + a = 174\).

- The third condition states that \((c + a) / 2 + b = 180\).

- Solve these equations:

- From the first equation: \( a + b + 2c = 336 \).

- From the second equation: \( 2a + b + c = 348 \).

- From the third equation: \( a + 2b + c = 360 \).

- Add all equations: \( 4a + 4b + 4c = 1044 \).

- Simplify: \( a + b + c = 261 \).

- The average is: \( 261/3 = 87 \).

- Option 1: Incorrect. Average is not 86.

- Option 2: ?? CORRECT! The average is 87.

- Option 3: Incorrect. Average is not 89.

- Option 4: Incorrect. Average is not 84.

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