$frac{3}{4}$ th of one number is equal to $frac{3}{5}$ th of the second number. If the difference between both the numbers is 105, then what is 50% of the first number?

Let the first number be x and the second number be y.

According to the question,

$frac{{3x}}{4} = frac{3}{5}y$

$Rightarrow frac{x}{4} = frac{y}{5}$

$Rightarrow y = frac{{5x}}{4}$

$herefore frac{{5x}}{4} - x = 105$

$Rightarrow frac{{5x - 4x}}{4} = 105$

$Rightarrow frac{x}{4} = 105$

$Rightarrow x = 105 imes 4 = 420$

$herefore 50;{ m{\% ;of;}}420 = frac{{420 imes 50}}{{100}} = 210$