Note-books are bought at $16$ for $\text{₹}700$ and sold at $11$ for $\text{₹}500$. How many notebooks should be sold to gain $\text{₹}450$?

To make calculation simple, let us choose a common number of notebooks by taking the LCM of $16$ and $11$, which is $16\times 11=176$.Cost Price (CP) of $16$ notebooks = $\text{₹}700$ $
$\text{CP of }176\text{ notebooks}=\frac{700}{16}\times 176=700\times 11=\text{₹}7700$$SellingPrice(SP)of$ 11$notebooks=$ \text{₹}500
$\text{SP of } 176 \text{ notebooks} = \frac{500}{11} \times 176 = 500 \times 16 = \text{₹}8000
The total gain obtained from selling $176$ notebooks is:
$$\text{Gain}=\text{SP}-\text{CP}=8000-7700=\text{₹}300$$
Now, using the unitary method:To gain $\text{₹}300$, number of notebooks to be sold = $176$ To gain $\text{₹}450$, number of notebooks to be sold = $\frac{176}{300}\times 450=176\times 1.5=264$