If the average of 5 positive integers is 45 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?  Choose the correct choice from the following answers.
A) 50
B) 53
C) 49
D) 48
E) 44

Rationale: "sum of 5 integer ( a , b , c , d , e ) = 5 * 45 = 225 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 225 i . e . 5 a = 215 i . e . a = 43 i . e . largest e = 43 + 10 = 53 answer : option b"
Answer: B