in a solvent 50% of benzoic acid dimerises while the rest ionises. determine molar mass of acid which is observed and also its van't hoff factor.

Your friend is correct.
Formula to calculate i ( Van't haff factor) using $\alpha$ (degree of ionizaion) is as follows:
i = (​1-$\alpha$) + $\frac{\alpha }{n}$
Here, 
$\alpha$ = 50/100 = 0.5
n ​= 2 (dimerisation)
i = (1.0-0.5) + 0.5/2
 = 0.75

i = $\frac{\mathrm{Observed} \mathrm{molar} mass}{\text{Actual Molar mass}}$

0.75 = $\frac{\mathrm{Observed} \mathrm{molar} mass}{122 \text{g/mol}}$

Observed Molar mass = 0.75 x 122 g/mol
                                  = 91.5 g/mol