Question 125

Three different numbers are chosen such that when each of the numbers is added to the average of the remaining two, the number 65, 69 and 76 are obtained. The average of the three original numbers is

Solution

Let the three original numbers be $$x,y,z$$

According to ques, => $$x+(\frac{y+z}{2})=65$$

Similarly, $$y+(\frac{x+z}{2})=69$$

and $$z+(\frac{y+x}{2})=76$$

Adding all the equations, => $$(x+y+z)+(x+y+z)=65+69+76$$

=> $$x+y+z=\frac{210}{2}=105$$

Dividing both sides by 3, => $$\frac{x+y+z}{3}=\frac{105}{3}=35$$

$$\therefore$$ Required average = 35

=> Ans - (A)

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