How to find the number in the set only with their average and with the other average when particular number is removed from the set?

Question

Let N be a set of some positive integer numbers with an average of 20 and containing the number 80. The number may or may not be distinct. However if one number equal to 80 is removed, the average drops to 18. What is the largest number that can possibly be contained in that set?

Answer 1

Hint. Step 1 is to find how many numbers are in the collection. Suppose there are $n$ initially. Then their total is $20n$. After removing 80, the total must be $20n-80$. There are now $n-1$ numbers with an average of 18, so the new total also equals $18n-18$. Hence $20n-80=18n-18$, so $n=31$.

Thus after removing the 80, we are left with 30 numbers totalling 540. Can you finish?

Answer 2

20 N - 80 = 18( N - 1 )

2N = 62

N = 31

30 * 18 = 540

So, 31 * 20 = 620

Largest Possible Number is: 620 - 80 - 1 * (Remaining Numbers)

i.e X = ( 620 - 80 - 1 * 29 )

Answer is : 511 !