Question

In a school library, the ratio of mathematics books to science books is the same as the ratio of science books to Hindi books. If there are \[450\] books in science and \[300\] books in Hindi, find the number of books in mathematics.

Answer 1

Hint: In this question, we have to find the number of books in mathematics.
First we need to take a random variable as the number of books in mathematics, then equating the ratios found using the given values of science and Hindi books to the ratio of science and maths books we can find out the required solution.

Formula used: If \[a:b\] and \[c:d\] are in the same ratio, we say that \[\dfrac{a}{b} = \dfrac{c}{d}\]

Complete step-by-step answer:
It is given that, in a school library, the ratio of mathematics books to science books is the same as the ratio of science books to Hindi books.
Also given that, there are \[450\]books in science and \[300\]books in Hindi.
We have to find out the number of books in mathematics.
Let us consider the number of books in mathematics as \[x\].
Then, from the given information we get,
\[x:450\] and \[450:300\] are in the same ratio, we get
$\Rightarrow$\[\dfrac{x}{{450}} = \dfrac{{450}}{{300}}\]
Let us multiply by \[450\] on both sides we get,
$\Rightarrow$\[x = \dfrac{{450 \times 450}}{{300}}\]
By cancelling the terms in it we get,
$\Rightarrow$\[x = 45 \times 15\]
That is \[x = 675\]

Hence the number of books in mathematics in the library is \[675\].

Additional Information: A ratio compares values. A ratio says how much of one thing there is compared to another thing.
A ratio shows the relative sizes of two or more values.
Ratios can be shown in different ways:
Using the “:” to separate example values.
 Using the “/” to separate one value from the total.
As a decimal, after dividing one value by the total.
As a percentage, after dividing one value by the total.

Note: In the given question it is provided that the ratio between two things are equal. Here we should be careful because this does not imply that the number of books are not the same. Suppose the ratios are not the same, we should do other methods to complete the required answer.