Suppose milk is sold at the rates of $5.50$, $6.00$, $5.75$ and $5.25$ rupees per litre in four different months. Assuming that equal amount of money are spent on milk by a family in the four months, the average price in rupees per litre will be:

Since an equal amount of money is spent in each of the four months, the average price per litre is given by the Harmonic Mean of the individual rates.
Let the amount spent each month be $M$ rupees.

* Quantity in month 1 = $\frac{M}{5.50}$
* Quantity in month 2 = $\frac{M}{6.00}$
* Quantity in month 3 = $\frac{M}{5.75}$
* Quantity in month 4 = $\frac{M}{5.25}$

$$\text{Total quantity}=M\left(\frac{1}{5.50}+\frac{1}{6.00}+\frac{1}{5.75}+\frac{1}{5.25}\right)$$

$$\text{Total amount spent}=4M$$

$$\text{Average Price}=\frac{\text{Total Amount}}{\text{Total Quantity}}=\frac{4}{\frac{1}{5.50}+\frac{1}{6.00}+\frac{1}{5.75}+\frac{1}{5.25}}$$

Let's convert the decimals into fractions:

* $5.50=\frac{11}{2}⟹\frac{1}{5.50}=\frac{2}{11}\approx 0.1818$
* $6.00=6⟹\frac{1}{6.00}=\frac{1}{6}\approx 0.1667$
* $5.75=\frac{23}{4}⟹\frac{1}{5.75}=\frac{4}{23}\approx 0.1739$
* $5.25=\frac{21}{4}⟹\frac{1}{5.25}=\frac{4}{21}\approx 0.1905$

Summing up the values:

$$\text{Sum}\approx 0.1818+0.1667+0.1739+0.1905=0.7129$$

Now computing the final average price:

$$\text{Average Price}\approx \frac{4}{0.7129}\approx 5.6108\text{rupees/litre}$$

Rounding to two decimal places gives $5.61$.