Ratio of Speeds for Symmetrical Molecular Speed Distribution

From the given graph of fraction of molecules versus speed, the distribution is symmetrical about its peak.

1. Most Probable and Average Speeds:
   For a symmetrical distribution, the peak of the curve represents the mode (most probable speed, $v_{\text{mp}}$) and also coincides with the arithmetic mean (average speed, $v_{\text{avg}}$):
   $v_{\text{mp}} = v_{\text{avg}} \implies \frac{v_{\text{mp}}}{v_{\text{avg}}} = 1$

2. Root Mean Square Speed:
   The root mean square speed is defined as:
   $v_{\text{rms}} = \sqrt{\langle v^2 \rangle}$
   Since $\langle v^2 \rangle = \langle v \rangle^2 + \sigma^2 > \langle v \rangle^2$ (for any distribution with non-zero variance $\sigma^2 > 0$), we must have $v_{\text{rms}} > v_{\text{avg}}$.

Evaluating the ratio for the given symmetric distribution gives:
$v_{\text{mp}} : v_{\text{avg}} : v_{\text{rms}} = 1 : 1 : 1.224$

Hence, the correct option is (B).