Question

Weight of 15 identical books is 6 kg. What is the weight of 45 such books? \[\]

Answer 1

Hint: We recall unitary method and direct variation because the given problem is in direct variation with quantities total weight of books say $a$ and number of books say $b$. We use the unitary method and first find the weight of a single book $\dfrac{a}{b}$ and then multiply 45 to find the required weight. \[\]

Complete step by step answer:
We know that the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. There are two types of two types of unitary method one is direct variation and other is indirect variation. \[\]
When one quality $a$ increases with another quantity $b$ and also $a$ decreases with $b$ then we say the quantities $a$ and $b$ are in direct variation. Here the fraction $\dfrac{a}{b}$ always remains constant. We divide the increasing quantity $a$ by $b$ to obtain the value of a single unit and then multiply to find the required value. \[\]
We are given the question that the weight of 15 identical books is 6kg. The books are identical which means all of them have equal weight. The total weight of the books increases with the number of books. So the problem is in direct variation. Let us denote the total weight of the books as $a$ and with the number of books as $b$. The weight of 1 single book is the value of a single unit here. So let us divide $a$ by $b$ and find the weight of 1 single book in kg as
\[\dfrac{a}{b}=\dfrac{6}{15}\]
We are asked to find the weight of 45 such books. We multiply 45 to the weight of 1 single book and find the required weight in kg as
\[45\times \dfrac{6}{15}=18\]

So, the correct answer is “18Kg”.

Note: : We need to be careful of the confusion between direct and indirect variation where $a$ decreases with increase in $b$ and $ab$ remains constant. The problems prices, weight come under direct ration while the problems of speed and time, men and work come under indirect variation.