Question

If \[15\] oranges cost \[Rs.35\], what is the cost of \[39\] oranges?

Answer 1

Hint: In order to find the cost of \[39\] oranges, we must assign the cost of \[39\] oranges a variable firstly. We can observe that the given relation between the oranges and the cost is in direct proportion. So in order to find the cost, we will be applying the method of proportion to the given quantities and cost.

Complete step by step answer:
Now let us briefly discuss proportions. . Proportion is nothing but saying that two ratios are equal. Two ratios can be written in proportion in the following ways- \[\frac{a}{b}=\frac{c}{d}\] or \[a:b=c:d\]. From the second way of notation, the values on the extreme end are called as extremes and the inner ones as means. Proportions are of two types: direct proportions and indirect or inverse proportions. In the direct proportion, there would be a direct relation between the quantities. In the case of indirect proportion, there exists an indirect relation between the quantities.
Now let us find the cost of \[39\] oranges.
Let us consider the cost of \[39\] oranges as \[x\].
We are given that,
Cost of \[15\] oranges is \[Rs.35\].
Now let us express it using the proportionality theorem.
\[\Rightarrow 15:39::35:x\]
Now let us solve it, we get
\[\begin{align}
  & \Rightarrow 15:39::35:x \\
 & \Rightarrow 15x=35\times 39 \\
 & \Rightarrow x=\frac{35\times 39}{15} \\
 & \Rightarrow x=91 \\
\end{align}\]
\[\therefore \] The cost of \[39\] oranges is \[Rs.91\]

Note: Before performing the operations, we must always check if the given quantities or comparisons are in direct or indirect proportion. We can use ratios and proportions in our daily life. We can apply a ratio for adding the quantity of milk to water or water to milk. We can apply proportions for finding the height of the buildings and trees and many more.