Explanation

(b)
Required two digit numbers are 12, 19, …,96 which leave a remainder 5 when they are divided by 7.
Here, $a = 12,\ d = 7,\ l = 96$
$\therefore$ $l = a + (n - 1)d$
$\Rightarrow$ $96 = 12 + 7(n - 1)$
$\Rightarrow$ $n = 13$
$\therefore$ $S_{13} = \frac{13}{2}(12 + 96) = \frac{13 \times 108}{2} = 702$