In a group of people, $\frac{7}{24}$th of them like only Continental food, $\frac{19}{60}$th of them like only Mediterranean food, and the rest like both. What is the total number of people in the group, if the number of people who like both Continental and Mediterranean food is $235?$

The correct option is C $600$
Let $‘‘x^{\prime \prime }$ be the total number of people.
People who like only Continental food $+$ People who like only Mediterranean food $+$ People who like both $=x$
$\frac{7}{24}\times x+\frac{19}{60}\times x+235=x$
$235=x-\frac{7}{24}\times x-\frac{19}{60}\times x$
$235=x(1-\frac{7}{24}-\frac{19}{60})$ [Distributive property]
$235=x\left(\frac{120-7\times 5-19\times 2}{120}\right)$
$235=x\left(\frac{120-35-38}{120}\right)$
$235=x\left(\frac{47}{120}\right)$
$x=\frac{235\times 120}{47}$
$x=5\times 120$
$x=600$
Thus, the total number of people in the group is $600$.