Question

A pile of Class-V Mathematics books has thickness of $ 14\dfrac{2}{5}{\text{ cm}} $ . If each book is $ 1\dfrac{1}{5}{\text{ cm}} $ thick, find how many books make up the pile.

Answer 1

Hint: This question is based on Fractions. In this question, we have given the thickness of a pile of books and the thickness of each book in the pile and we have to find the number of the books that make up the pile. Also, the thickness of the books is given in mixed fraction form. The mixed fraction numbers are the combination of a whole number and a fraction number. For example, $ 2\dfrac{3}{4} $ is a mixed fraction number and it can be written as,
 $
2\dfrac{3}{4} = \dfrac{{\left( {4 \times 2} \right) + 3}}{4}\\
2\dfrac{3}{4} = \dfrac{{11}}{4}
$

Complete step-by-step answer:
Let the thickness of a pile of Class-V Mathematics books be $ T $ and the thickness of each book in the pile be $ t $ .
Then, we have given,
The thickness of a pile of Class-V Mathematics books
 $
\Rightarrow T = 14\dfrac{2}{5}{\text{ cm}}\\
\Rightarrow T = \dfrac{{72}}{5}{\text{ cm}}
$
And, the thickness of each book in the pile
 $
\Rightarrow t = 1\dfrac{1}{5}{\text{ cm}}\\
\Rightarrow t = \dfrac{6}{5}{\text{ cm}}
$ .
Now according to the question,
The thickness of a pile of Class-V Mathematics books = (Number of books in the pile $ \times $ the thickness of each book in the pile)
So,
Where, $ n $ is the number of books in the pile.
Substituting the values of $ T $ and $ t $ in the equation we get,
Solving this we get,
 $ n = 12 $
Therefore, there are $ 12 $ books in the pile.
So, the correct answer is “$ 12 $”.

Note: It should be noted that if any value is given in the mixed fraction form, we should always change it into either simple fractions or decimal numbers because calculations in the fraction form or decimal form are easy compared to the mixed fraction form.