Harry bought a cup of mixed flavour ice cream. If $\frac{1}{8}$th of the ice-cream was chocolate, $\frac{5}{12}$th was vanilla, $\frac{7}{16}$th was mint and the rest was caramel, then what fraction of the ice-cream was caramel?

The correct option is D

$\frac{1}{48}$

Fraction of chocolate icecream =$\frac{1}{8}$
Fraction of Vanilla ice cream = $\frac{5}{12}$
Fraction of Mint ice cream = $\frac{7}{16}$

Whole Ice Cream = Chocolate + Vanilla + Mint + Caramel
$\Rightarrow 1=\frac{1}{8}+\frac{5}{12}+\frac{7}{16}+Caramel$
Thus, the fraction of caramel ice cream
$=1-(\frac{1}{8}+\frac{5}{12}+\frac{7}{16})$

LCM of the denominators = 48
$\frac{1}{8}+\frac{5}{12}+\frac{7}{16}$ $=\frac{1\times 6}{8\times 6}+\frac{5\times 4}{12\times 4}+\frac{7\times 3}{16\times 3}=\frac{6+20+21}{48}=\frac{47}{48}$

Fraction of caramel ice cream $=1-\frac{47}{48}=\frac{48-47}{48}=\frac{1}{48}$