A sum of ₹8,520 is divided between A, B, C and D in the ratio $\frac{1}{2}:\frac{1}{4}:\frac{2}{5}:\frac{5}{8}$. What is the difference between shares of B and D?

Given ratio of A : B : C : D is:
$$\frac{1}{2}:\frac{1}{4}:\frac{2}{5}:\frac{5}{8}$$
To convert this into a whole-number ratio, multiply each term by the LCM of denominators $(2,4,5,8)$, which is $40$:
$$\text{A}=\frac{1}{2}\times 40=20$$
$$\text{B}=\frac{1}{4}\times 40=10$$
$$\text{C}=\frac{2}{5}\times 40=16$$
$$\text{D}=\frac{5}{8}\times 40=25$$
So, the ratio is $\text{A}:\text{B}:\text{C}:\text{D}=20:10:16:25$.Sum of the ratio units = $20+10+16+25=71$ units.Total sum = ₹8,520.
$$71\text{ units}=8520⟹1\text{ unit}=\frac{8520}{71}=120$$
The difference between the shares of B and D = $25-10=15$ units.
$$\text{Difference}=15\times 120=\text{₹}1,800$$