A vendor buys $20$ pens for ₹$15$ and sells them at $15$ for ₹$20$. How many pens should be bought and sold to earn a profit of ₹$245$?

To make calculation easier, let's take LCM of number of pens bought ($20$) and sold ($15$).LCM of $20$ and $15=60$.Cost Price (CP) of $20$ pens = ₹$15$ CP of $60$ pens = $15\times 3=$ ₹$45$ Selling Price (SP) of $15$ pens = ₹$20$ SP of $60$ pens = $20\times 4=$ ₹$80$ Profit on $60$ pens = $\text{SP}-\text{CP}=80-45=$ ₹$35$ To earn a profit of ₹$35$, number of pens needed = $60$ To earn a profit of ₹$245$, number of pens needed:
$$\text{Number of pens}=\frac{60}{35}\times 245=60\times 7=420$$