 QUESTION

# The ratio of story books in a library to other books is 1:7. The total number of story books is 800. Find the total number of books in a library.

Hint: Assume the books are in the multiple of ‘x’ therefore you will get ‘x’ as the number of story books. Then put this value of ‘x’ in the number of other books you will get its value. Then add the values of story books and other books to get the final answer.

To solve the given question we will write the given data first,

The ratio of story books to other books = 1:7 ………………………………………… (1)

Total number of story books in library = 800 ………………………………………….. (2)

We will assume that the number of books is in the multiple of ‘x’ therefore by referring equation (1) we can write,

Total number of story books = $1\times x$

Therefore, Total number of story books = x ………………………………………………… (3)

Also the total number of other books = 7x ………………………………………………………... (4)

Now if we compare equation (3) with equation (2) we will get,

Therefore, 800 = x

By rearranging the above equation we will get,

Therefore, x = 800

If we put the value of ‘x’ in equation (4) we will get,

Total number of other books = $7\times 800$

Therefore, the total number of other books = 5600 ………………………………………………. (5)

As we have asked for total number of books therefore we should consider story books also,
therefore we will get,

Total number of books in the library = Total number of story books + Total number of other books

If we put the values of equation (2) and equation (5) in the above equation we will get,
Total number of books in the library = 800 + 5600

Therefore, total number of books in the library = 6400

Therefore there are 6400 books present in the library.

Note: There is a chance of committing silly mistakes by considering the number of other books as the total number of books in the library. Therefore be aware while solving as the total number of books in the library includes story books also.