Question

A bookshelf holds both paperback and hardcover books. The ratio of paper back books to hardcover books is $22$ to $3$. How many paperback books are on the shelf ?

If $18$ paperback books were removed from the shelf and replaced with $18$ hardcover books, the resulting ratio of paperback books to hardcover books on the shelf would be $4$ to $1$

• A. $158$
• B. $200$
• C. $198$
• D. $164$

Answer 1

The correct option is C $198$

The question stem states that the ratio of paperback books to hardcover books initially is $22$ to $3$.

So, let us assume the no. of paperback books and hardcover books be $22x$ and $3x$ respectively.

Now, according to given conditions,

$\frac{22x-18}{3x+18}=\frac{4}{1}$

Cross-multiply both the sides,

$22x-18=4(3x+18)$

$22x-18=12x+72$

$22x-12x=72+18)$

$10x=90$

$x=9$

So, the number of paperback books = $22x$ = $22\times 9$ = $198$

Option C