The total number of two-digit numbers ‘n’, such that$3^n+7^n$ is a multiple of 10, is……

$3^n+7^n$is a multiple of 10, It is possible when  is odd. 

            Since n is odd, n=$\left\{11,13,15,\mathrm{.......99}\right\}$

            Number of values of n = 45