45.88 % (approx.)

Suppose, Salim’s Gross Income = 2x
Kashem’s Gross Income = 2x x $\frac{1}{2}$= x

Two years ago, Kashem’s Basic salary = x of 70% = x x $\frac{70}{100}$= 0.7x
After a raise of 5% in his annual basic salary for next 2 years,
His current Basic salary = 0.7x x (1.05)²
Since his allowances, which are 30% of his Gross income, have remain unchanged
Kashem’s current gross income = 0.7x x (1.05)² + 0.3x = 1.071752x
Similarly, Selim’s Present Basic salary = (2 x 0.8) x (1.10)²
Since his allowances, which are 20% of his Gross income, have remain unchanged
Selim’s current gross income = (2x x 0.8) x (1.10)² + (0.2 x 2x) = 2.336x
$\frac{\textbf{Kashem’s gross income}}{\textbf{Selim’s gross income}}= \frac{1.07175x}{2.33x}$ = 0.4588 = 45.88%