Question

One litre of petrol costs Rs. \[63\dfrac{3}{4}\]​. Find the cost 34 litres of petrol.

Answer 1

Hint: In this question, we are given that the cost of one litre of petrol is Rs. \[63\dfrac{3}{4}\]. Then in order to determine the cost of \[x\] litres of petrol, we have to multiply the cost of one litre of petrol with \[x\].
So in order to find the cost of 34 litres of petrol, we have to multiply the cost of one litre of petrol with 34. Then after doing some calculations, we will get the desired answer.

Complete step by step answer:
We are given the details that the cost of one litre of petrol is Rs. \[63\dfrac{3}{4}\].
Since we know that an improper fraction \[a\dfrac{b}{c}\] can also be written as a proper fraction which is given by \[\dfrac{ac+b}{c}\].
Therefore we will first simplify the cost of one litre of petrol , that is Rs. \[63\dfrac{3}{4}\] into a proper fraction.
That is we have
\[\begin{align}
  & 63\dfrac{3}{4}=\dfrac{63\times 4+3}{4} \\
 & =\dfrac{255}{4}
\end{align}\]
Hence the cost of one litre of petrol is given by Rs.\[\dfrac{255}{4}\].
Now since we know that if we want to determine the cost of \[x\] litres of petrol, we have to multiply the cost of one litre of petrol with \[x\].
So in order to find the cost of 34 litres of petrol, we have to multiply the cost of one litre of petrol with 34.
Thus, the cost of 34 litres of petrol is given by
\[34\times \dfrac{255}{4}\]
Now on calculating the above expression, we get
\[\begin{align}
  & 34\times \dfrac{255}{4}=\dfrac{34\times 255}{4} \\
 & =\dfrac{8670}{4}
\end{align}\]
We can further divide the above expression by 2 to get,
\[\dfrac{8670}{4}=\dfrac{4335}{2}\]
Now again we can convert the proper fraction \[\dfrac{b}{c}\] into an improper fraction which is given by \[q\dfrac{r}{c}\] where \[q\] is the quotient when \[b\] is divided by \[c\] and \[r\] is the remainder.
Since we can have
\[4335=2\times 2167+1\]
That is 2167 is the quotient when 4335 is divided by 2 and 1 is the remainder.
Therefore we have
\[\dfrac{4335}{2}=2167\dfrac{1}{2}\]

Hence the cost of 34 litres petrol is given by Rs, \[2167\dfrac{1}{2}\].

Note: In this problem, in order to determine the cost of 34 litres petrol given that one litre of petrol costs Rs. \[63\dfrac{3}{4}\]​ please take we have the change the improper fractions to proper fractions and vice versa in order to do the calculations. But then we have to change the fraction to an improper fraction again or to get the answer in order to make it in the form which is given in the question.