Question

A car runs 16 km using 1 litre of petrol. How much distance will it cover using $2\dfrac{3}{4}$ litres of petrol?

Answer 1

Hint: Convert the given mixed fraction of petrol into improper fraction by using the formula: $a\dfrac{b}{c}=\dfrac{a\times c+b}{c}$. Now, find the total distance the car will cover by multiplying the distance covered by the car using 1 litre of petrol by the total volume of petrol.

Complete step-by-step solution -
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. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple. For example: suppose the value of 10 pencils is Rs. 20, and we have to find the value of 50 pencils. What we have to do is, find the value of a single pencil by dividing total pencils with total rupees. In this way we will get the value of 1 pencil, then multiply this value with the total number of pencils whose cost we have to find. So, in the above example the value of 1 pencil will be Rs. 2 and therefore the value of 50 pencils will be $2\times 50=100$ rupees.
Now, in the given question, we already have been provided with the distance covered by the car using 1 litre of petrol.
Now, changing the given mixed fraction into improper fraction, we get,
Total volume of petrol $=2\dfrac{3}{4}=\dfrac{4\times 2+3}{4}=\dfrac{11}{4}\text{ litres}$.
Therefore, distance travelled by the car using $\dfrac{11}{4}$ litres of petrol
$\begin{align}
  & =16\times \dfrac{11}{4} \\
 & =4\times 11 \\
 & =44\ \text{km} \\
\end{align}$

Note: We have applied a unitary method because it is the easiest approach to solve this question. Here, we were not required to find the distance travelled by the car using 1 litre of petrol because it was already provided to us. But if it is not given, we have to find it with the help of given information just like we saw in the example.