What is the sum of all two digit numbers that gives a remainder of 3 when they are divided by 7?

Solution (By Examveda Team)

The two digit number which gives a remainder of 3 when divided by 7 are:
10, 17, 24 ..... 94.
Now, these number are in AP series with
1st Term, a = 10;
Number of Terms, n = 13;
Last term, L = 94 and
Common Difference, d = 7.
Sum,
$$\eqalign{ & = \left\{ {{\text{n}} \times \frac{{{\text{a}} + {\text{L}}}}{2}} \right\} \cr & = 13 \times 52 \cr & = 676 \cr} $$