$5\mathrm{ml}$ of $1\mathrm{N} \mathrm{HCl}, 20\mathrm{ml}$ of $\frac{\mathrm{N}}{2} {\mathrm{H}}_2{\mathrm{SO}}_4$ and $30\mathrm{ml}$ of $\frac{\mathrm{N}}{3} {\mathrm{HNO}}_3$ are mixed together and the volume is made to one litre. The normality of the resulting solution is

The correct option is (d) $\frac{\mathrm{N}}{40}$

We know that

According to the neutralization law,

$\mathrm{NV}={\mathrm{N}}_1{\mathrm{V}}_1+{\mathrm{N}}_2{\mathrm{V}}_2+{\mathrm{N}}_3{\mathrm{V}}_3$

${\mathrm{N}}_1$= normality of $\mathrm{HCl}$

${\mathrm{V}}_1$=volume of $\mathrm{HCl}$

${\mathrm{N}}_2$= normality of  ${\mathrm{H}}_2{\mathrm{SO}}_4$

${\mathrm{V}}_2$= volume of  ${\mathrm{H}}_2{\mathrm{SO}}_4$

${\mathrm{N}}_3$= normality of  ${\mathrm{HNO}}_3$

${\mathrm{V}}_3$= volume of  ${\mathrm{HNO}}_3$

$\mathrm{N}\times 1000=1\times 5+\frac{1}{2}\times 20+\frac{1}{3}\times 30=5+10+10=25$

$\mathrm{N}=0.025=\frac{\mathrm{N}}{40}$= Normality of the resulting solution.