Proportional Reasoning - 2 | FIO

Question 2

A school library has books in different languages in the following ratio — no. of Odiya books : no. of Hindi books : no. of English books :: 3 : 2 : 1. If the library has 288 Odiya books, how many Hindi and English books does it have?

Solution

We can use the given ratio and the number of one type of book to find the value of each part in the ratio.

Step 1 — Find the value of one ratio part

The problem gives us the ratio of books. The ratio shows parts for each language. Odiya books are 3 parts. Hindi books are 2 parts. English books are 1 part. Let $k$ represent one part of this ratio. So, the number of Odiya books is $3k$ . The number of Hindi books is $2k$ . The number of English books is $1k$ . We know there are 288 Odiya books. We can set up an equation to find $k$ .

$3k = 288$

$k = \frac{288}{3}$

$\boxed{k = 96}$

Step 2 — Calculate the number of Hindi and English books

Now we know that one part ( $k$ ) equals 96 books. We can find the number of Hindi books. Hindi books are 2 parts of the ratio.

$\text{No. of Hindi books} = 2 \times k$

$= 2 \times 96$

$\boxed{\text{No. of Hindi books} = 192}$

Next, we find the number of English books. English books are 1 part of the ratio.

$\text{No. of English books} = 1 \times k$

$= 1 \times 96$

$\boxed{\text{No. of English books} = 96}$

Answer

(i) The library has 192 Hindi books. (ii) The library has 96 English books.

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