A mixture of $NaOH$  and $N{a}_{2}C{O}_3$ required 25mL of 0.1 M HCl using phenolphthalein as the indicator. However, the same amount of the mixture requied 30 mL HCl using methyl orange was used as the indicator. The molar ratio of $NaOH$ and  $N{a}_{2}C{O}_3$ in the mixture is x:y. Then the x+y is (x and y are integers)

With Phenolphthalein indicator

 m. eq of $NaOH+\frac{1}{2}m.$ eq of $N{a}_{2}C{O}_3=$m. eq of $HCl$

$x+\frac{y}{2}=25\times 0.1\times 1$$\Rightarrow x+0.5y=2.5\to 1$

 With methyl orange indicator m.eq of NaOH+m.eq of Na₂CO₃=m.eq of HCl

$x+y=30\times 0.1\times 1$$\Rightarrow x+y=3\to 2$

Solving 1 and 2 $y=1$  and $x=2$

but equivalents = moles $\times n-f$ 

 $\because$ for $N{a}_{2}C{O}_3$             $1=mole\times 2$             

                                          mole =0.5

 for $NaOH$: 2= moles $\times 1$            $\Rightarrow moles=2$                     

 ration of moles of: $NaOH:N{a}_{2}C{O}_3$

                             2 : 0.5

                           4 :1

                   x+y=4+1=5