In a library the ratio of story books and other books is 7 : 2 and there are 1512 story books. Due to collection of some more story books the ratio becomes 15 : 4. The number of story books collected is = ?

Explanation:-

According to the question, $$\eqalign{ & \frac{{{\text{Story books}}}}{{{\text{Other books}}}} = \frac{7}{2} \cr & {\text{Story books = 1512}} \cr & {\text{7 units}} \to 1{\text{512}} \cr & {\text{1 unit}} \to \frac{{1512}}{7} = 216 \cr & {\text{2 units}} \to 216 \times 2 = 432 \cr & {\text{Other books }} = 432 \cr & {\text{New ratio of}} \cr & \frac{{{\text{Story books}}}}{{{\text{Other books}}}} = \frac{{15}}{4} \cr}$$ As we know that only story books are added
$$\eqalign{ & {\text{4 units}} \to 43{\text{2}} \cr & {\text{1 unit}} \to \frac{{432}}{4} = 108 \cr & {\text{15 units}} \to 108 \times 15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1620 \cr}$$ New collection of story books = 1620
∴ NUmber of story books are added = 1620 - 1512 = 108