Question

In a school library, the ratio of General Knowledge books to Mathematics is the same as the ratio of Mathematics books to Physics books. If there are 150 books of General Knowledge and 300 books of Mathematics, find the number of Physics books.

Answer 1

Hint: First of all, consider the total number of books of Physics to be P. Then find the ratio of the General Knowledge books to Mathematics books and equate it to the ratio of Mathematics books to Physics books to get the value of P.

Complete step-by-step answer:
We are given that in the school library, the ratio of General Knowledge books to Mathematics books is the same as the ratio of Mathematics books to Physics Books. If there are 150 books of General Knowledge and 300 books of Mathematics, we have to find the number of books of Physics.
First of all, let us consider the number of books of Physics in the library to be P. We are given that the number of books of General Knowledge in the library is 150. Also, we are given that the number of books of Mathematics in the library is 300. So, the ratio of General Knowledge books to Mathematics Books is \[=\dfrac{\text{Number of General Knowledge Books}}{\text{Number of Mathematics Books}}\].
By substituting the values of the number of General Knowledge books = 150 and number of Mathematics books = 300 in the above expression, we get the ratio of General Knowledge books to Mathematics books \[=\dfrac{150}{300}\]. By simplifying the ratio, we get the ratio of General Knowledge books to Mathematics Books \[=\dfrac{1}{2}....\left( i \right)\].
Also, the ratio of Mathematics Books to Physics books \[=\dfrac{\text{Number of Mathematics Books}}{\text{Number of Physics Books}}\]. By substituting the values of the number of Mathematics books = 300 and the number of Physics Books = P in the expression, we get the ratio of Mathematics books to Physics books = \[\dfrac{300}{P}....\left( ii \right)\].
Now we are given that the ratio of General Knowledge books to Mathematics books is equal to the ratio of Mathematics books to Physics books. So, we can write in equation form as: The ratio of General Knowledge books to Mathematics Books = Ratio of Mathematics Books to Physics Books. By substituting the values of LHS and RHS from equation (i) and (ii) respectively in the expression, we get \[\dfrac{1}{2}=\dfrac{300}{P}\]. By cross multiplying, we get \[P=300\times 2\Rightarrow 600\text{ books}\].
So, we get the number of Physics books in the school library equal to 600.

Note: In this question, many students make the mistake of writing wrong ratios that is, in place of \[\dfrac{300}{P}\], sometimes they write \[\dfrac{P}{300}\] or instead of \[\dfrac{1}{2}\], they calculate it to be \[\dfrac{2}{1}\]. So students are advised to properly read the information given in the question first and then only proceed to a solution.