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We are given that average of three distinct integers is 28, that means the sum of these three integers is 28 × 3 = 84
Let us write x + y + z = 84
x, y, z being the three distinct integers in ascending order.
If the smallest number is increased by 7 and the largest number is reduced by 10
(x + 7) + (y) + (z – 10) = 81
New arithmetic mean will be 81/3 = 27
And this is said to be 2 more than the middle number, meaning
27 – 2y = 25
x + z = 59
We are given that difference between the largest and the smallest numbers becomes 64,
(z − 10) – (x + 7) = 64
z – x = 81
Adding the two equations we get, 2z = 140
z = 70