let 'x' the money the girl has in the beginning

a girl spend 1/2 of her money in a store: x/2

then she goes to another store and spends 1/2 of what was left with her: 1/2(x - x/2)

after that she has Rs 24

if add up all the money we get the total sum she has that is x

x/2 + (x - x/2)/2 + 24 = x

by solving the equation we find

x = $96

click here to see the step by step solution of the equation

the girl has $96 when she started.