Question

If 15 oranges cost $Rs.110$ , what do $39$ oranges cost $?$

Answer 1

Hint: Here in this question, we can use the unitary method to find the required cost. We can take a particular variable to each of the quantities mentioned in the question and then apply the method through which we can form an equation and then we can find our required answer. This is a simple question of proportionality.
Formula used: $\dfrac{{{y_1}}}{{{x_1}}} = \dfrac{{{y_2}}}{{{x_2}}}$

Complete step-by-step solution:
Let, ${x_1} = 15$oranges
${y_1} = \,Rs.110$
Similarly,
${x_2} = 39\,oranges$
Then, the cost of $39$ oranges being ${y_2}$.
According to the question,
Using formula,
$\dfrac{{{y_1}}}{{{x_1}}} = \dfrac{{{y_2}}}{{{x_2}}}$
Put the values of ${x_{1\,}},\,{x_2}\,and\,{y_1}.$
$\dfrac{{110}}{{15}} = \dfrac{{{y_2}}}{{39}}$
After cross-multiplication, we get
${y_2} = 110 \times \dfrac{{39}}{{15}}$
${y_2} = Rs.286$
Hence, the cost of $39\,oranges$ is $Rs.110$
Here, in this question $\dfrac{{110}}{{15}}$ is the cost of $1$ orange. So, simply multiply it with $39$ to find the cost of $39$ oranges.
Therefore, if the cost of $15$ oranges is $Rs.110$, then the cost of $39$ oranges will be $Rs.286$.

Note: This is a simple example of proportionality relation. Generally, in these types of questions, we have to calculate the quantity for a $1$ unit and then multiplying it with total numbers, we get the quantity for total numbers.