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 ?

Let the numbers are x, y and z.

As per the condition given in the question

$$\Rightarrow \dfrac{x+y}{2}+z=168$$ -------(i)

$$\Rightarrow \dfrac{y+z}{2}+x=174$$------(ii)

$$\Rightarrow \dfrac{z+x}{2}+y=180$$--------(iii)

From the equation (i), (ii) and (iii)

$$\dfrac{x+y+y+z+z+x}{2}+x+y+z=168+174+180$$

$$\Rightarrow 2(x+y+z)=522$$

$$\Rightarrow x+y+z=261$$

The average of the numbers $$=\dfrac{x+y+z}{3}$$

Now substituting the values, the required average $$=\dfrac{261}{3}=87$$