We know,

$${p_{Total}} = p_A^o \times {\chi _A} + p_B^o \times {\chi _B}$$

and for equimolar solutions $${\chi _A} = {\chi _B} = 1/2$$

Given, $${p_{total}} = 45$$ torr for equimolar solution and $$p_A^o = 20$$ torr

So, $$45 = p_A^o \times {1 \over 2} + p_B^o \times {1 \over 2} = {1 \over 2}(p_A^o + p_B^o)$$

or $$p_A^o + p_B^o = 90$$ torr ....... (i)

But we know $$p_A^o = 20$$ torr

So, $$p_B^o = 90 - 20 = 70$$ torr (From Eq. (i))

Now, for the new solution from the same formula

$${p_{total}} = 22.5$$ torr

$$22.5 = 20{\chi _A} + 70(1 - {\chi _A})$$ (As $${\chi _A} + {\chi _B} = 1$$)

or $$22.5 = 70 - 50{\chi _A}$$

So, $${\chi _A} = {{70 - 22.5} \over {50}} = 0.95$$

Thus, $${\chi _B} = 1 - 0.95 = 0.05$$ (as $$\chi$$_A + $$\chi$$_B = 1)

Hence, the ratio

$${{{\chi _A}} \over {{\chi _B}}} = {{0.95} \over {0.05}} = 19$$