An alloy consists of $27\dfrac{1}{2}$ kg of copper and $2\dfrac{3}{4}$ kg of tin. Find the ratio by weight of tin to the alloy.

Weight of alloy = Weight of tin + Weight of copper

$\therefore \text{Weight of alloy} = 27\dfrac{1}{2} + 2\dfrac{3}{4} \\[0.5em] = \dfrac{55}{2} + \dfrac{11}{4} \\[0.5em] = \dfrac{110 + 11}{4} \\[0.5em] = \dfrac{121}{4}$

Ratio by weight of tin to alloy = $\dfrac{\text{Weight of tin}}{\text{Weight of alloy}}$

$= \dfrac{\dfrac{11}{4}}{\dfrac{121}{4}} \\[0.5em] = \dfrac{11}{121} \\[0.5em] = \dfrac{1}{11}$

Hence, the ratio by weight of tin to alloy is 1 : 11.