Explanation

Here,
The ratio of prices of two books is 3\;:\;1\;.
And the price of the first book is ₹\;75.
Let, the price of the second book is ₹\;‘x’.
According to the question,
3\;:\;1=75\;:\;x
\rightarrow\large\frac{3}{1}\normalsize=\large\frac{75}{x}
\rightarrow 3x=\left(75\times1\right) _{[cross multiply]}
\rightarrow x=\large\left(\frac{75\times1}{3}\right)
\rightarrow x=25
So that, the price of the second book is ₹\;25.
If the price of the first book was ₹\;25 more then the required ratio :
\large\frac{75+25}{25}\normalsize=\large\frac{100}{25}\normalsize=\large\frac{4}{1} or 4\;:\;1
Ans: 4\;:\;1\;.

These particular math questions can also be asked in the following ways:

1. The prices of two books are in a ratio of 3:1. If the price of the first book is ₹75, what would be the ratio of their prices if the price of the first book increased by ₹25?
2. If the price of the first book is ₹75 and the ratio of prices of the two books is 3:1, what would be the new ratio of their prices if the price of the first book increased by ₹25?
3. The price of the first book is ₹75, and the ratio of prices of the two books is 3:1. If the price of the first book increases by ₹25, what would be the ratio of their prices?