2015/059) Problem Find the largest number

N and M are positive integers such that N+M=21. The largest possible value of $\dfrac{1}{N}+\dfrac{1}{M}$ is $\dfrac{a}{b}$ where $\dfrac{a}{b}$ is in lowest form.Find a+b.

Solution

$\dfrac{1}{N}+\dfrac{1}{M}$ = $\dfrac{N+M}{NM}$ =$\dfrac{21}{NM}$

This is largest when NM is lowest.

clearly when N= 1 and M= 20 ( or N = 20, M = 1)

so NM = 20

so a= 21 and b = 20 hence a+b = 41

I have solved at https://in.answers.yahoo.com/question/index?qid=20130408091854AAlkBX4