Question

The difference between the largest and the second largest of 3 numbers is added to the smallest number. Now, the average of the largest, second largest and the new number formed exceeds the average of the original 3 numbers by 5. The largest number exceeds the 2nd largest number by how much?

Answer 1

lets assume largest number is x

2nd largest is y

third number is z

now average of all 3 number is

A1 = (x +y+z)/3

new 3rd number = third number + difference of largest and 2nd largest number

= z + x -y

now average of new numbers are

A2 = (x +y+ z +x -y)/3

= (2x+z)/3

as per equation

A2 = A1 + 5

so

(x+y+z + x -y)/3= (x+y+z)/3 +5

(x +y+z+x-y)/3= (x +y+z+15)/ 3

cancelling denominator from both sode

x+y+z+(x-y) = x+y+z + 15

so x- y = x+y+z -x-y-z +15

so x - y = 15

so difference between largest and 2nd largest number is 15