Answer is C.
Detailed method of solving this problem.
Let Speed of Mahira be $S_{m}$ and Speed of Neelima be $S_{n}$
Relative Speed (${S_{m}} +S_{n}) = \frac{Dist\ travelled}{Time} = \frac{72}{6}=12 miles/hour$ → (1)
if the Dist traveled by Mahira be x, then the Dist traveled by Neelima be 72–x
Case 1 – When they meet each other, time taken by both are same
$\frac{Dist_{m}}{Speed_{m}} = \frac{Dist_{n}}{Speed_{n}}$
$\frac{x}{S_{m}} = \frac{72-x}{S_{n}}$ → (2)
Case 2 – After they meet each other, time taken by both are same
After meeting each other, Dist need to travel by Mahira will be 72-x, and Dist need to travel by Neelima will be x
$\frac{72-x}{S_{m}} = \frac{x}{S_{n}}$ → (3)
Substitute ${S_{n}} = \frac{72-x}{x}*S_{m}$ from equation (2) and ${S_{n}}$ = 12 – ${S_{m}}$ from (1) in equation (3).
$\frac{S_{n}}{S_{m}} = \frac{S_{m}-1}{S_{n}+1}$
$\frac{12-x}{x} = \frac{x-1}{12-x+1}$
On solving x, we will get 6.5 miles/hour is the speed of Mahira and 5.5 miles/hour is the speed of Neelima