Question

The weight of 56 books is 8 kg. What is the weight of 152 such books? How many such books weigh 5 kg?

Answer 1

Hint: We find the weight of one book by dividing total weight of books by total number of books. We multiply 152 to the weight of one book to get the first answer. We divide the number of books total weight to find how many books are there in 1 kg weight. We multiply 5 to get the number of books in 5kg weight.

Complete step by step solution:
We know in unitary method that when one quantity $a$ 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 56 books is 8 kg. The total weight of the books increases with total numbers of books. So we have to divide to find the value for a single unit. \[\]
So the weight of one book is
\[\dfrac{\text{total weight of books}}{\text{total number of books}}=\dfrac{8}{56}=\dfrac{1}{7}\text{ kg}\]
We are asked to find weight of 152 books which is
\[\text{weight of one book}\times \text{152=}\dfrac{1}{7}\times 152=21.714\text{ kg}\]
We are further how many books are in 5kg weight. The number of books also increases with more weights. So by again by direct vacation the value of single unit the numbers of books in 1 kg weight is
\[\dfrac{\text{total number of books}}{\text{total weight of books}}=\dfrac{56}{8}=7\]
So the number of books in 5kg weight is
\[\text{Number of books 1 kg weight}\times \text{5=}7\times 5=35\text{ }\]

Note: We note that if the quantity $a$ decreases with increase in quantity $b$ then we say $a,b$ are in direct variation and indirect variation we first multiply to find the value of a single unit. We see that problems like men and work, speed and time are in indirect variation while measurement length, weight or time-work problems are in direct variation.