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If N is two digit number. when digits a...

If N is two digit number. when digits are interchanged, we get another prime number M.If `N+M=176` then find `N-M`.

Text Solution

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Let `N` is `10x+y`.
Then, `M` will be `10y+x`.
`:. 10x+y+10y+x = 176`
`=>11x+11y = 176`
`=>x+y = 16`
So, possible values of `x` and `y` are `(9,7)`, or `(8,8)` or `(7,9)`.
When `x = 9, y = 7`, then `N = 97` and `M = 79`, which is a prime number.
`:. N-M = 97-79 = 18`
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