$m$ g of water at $30^{\circ} C$ is mixed with $5$ g of ice at $-20^{\circ} C$. If the final equilibrium temperature of the mixture is $6^{\circ} C$,find the value of $m$. (Given: specific heat capacity of ice $= 0.5 \text{ cal g}^{-1} {}^{\circ} C^{-1}$,specific heat capacity of water $= 1 \text{ cal g}^{-1} {}^{\circ} C^{-1}$,and latent heat of fusion of ice $= 80 \text{ cal g}^{-1}$) (in $g$)

• A
  $48$
• B
  $20$
• C
  $24$
• D
  $40$