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Hint: Here, we will use the formula to find the increased price,\[{\text{Increased Price}} = {\text{Actual Price}} + {\text{Increased Percentage}} \times {\text{Actual Price}}\]. Then we will take the increased price as the actual price and calculate the decreased price using the formula, \[{\text{Decreased Price}} = {\text{Actual Price}} - {\text{Decreased Percentage}} \times {\text{Actual Price}}\].

Apply these formulae, and then use the given conditions to find the required value.

We are given that the price of petrol is Rs. 65.

We know that the formula to find the increased price is \[{\text{Increased Price}} = {\text{Actual Price}} + {\text{Increased Percentage}} \times {\text{Actual Price}}\].

So we will now calculate the increased price of the car when increased by \[4\% \] using the above formula.

\[

{\text{Increased Price}} = 65 + \dfrac{4}{{100}} \times 65 \\

= 65 + \dfrac{{260}}{{100}} \\

= 65 + 2.6 \\

= {\text{Rs. }}67.6 \\

\]

Thus, the increased price of the car is Rs. \[67.6\].

Now we will take the increased price as the actual price to find the decrease price of the car.

We know that the decreased price is calculated using the formula,\[{\text{Decreased Price}} = {\text{Actual Price}} - {\text{Decreased Percentage}} \times {\text{Actual Price}}\].

We will now find the decreased price of the car after \[5\% \] reduction using the above formula.

\[

{\text{Decreased Price}} = 67.6 - \dfrac{5}{{100}} \times 67.6 \\

= 67.6 - \dfrac{{338}}{{100}} \\

= 65 - 3.38 \\

= {\text{Rs. }}61.62 \\

\]

Thus, the decreased price of the care is Rs. \[61.62\].

Therefore, the required price of the car is Rs. \[61.62\].

Note: In solving these types of questions, you should be familiar with the concept of increased price and decreased price. Students should also remember the properties of probability for ease. There is a fair possibility that the student uses the inverse of the formula and will end up getting the wrong answer.

Apply these formulae, and then use the given conditions to find the required value.

__Complete step by step answer__We are given that the price of petrol is Rs. 65.

We know that the formula to find the increased price is \[{\text{Increased Price}} = {\text{Actual Price}} + {\text{Increased Percentage}} \times {\text{Actual Price}}\].

So we will now calculate the increased price of the car when increased by \[4\% \] using the above formula.

\[

{\text{Increased Price}} = 65 + \dfrac{4}{{100}} \times 65 \\

= 65 + \dfrac{{260}}{{100}} \\

= 65 + 2.6 \\

= {\text{Rs. }}67.6 \\

\]

Thus, the increased price of the car is Rs. \[67.6\].

Now we will take the increased price as the actual price to find the decrease price of the car.

We know that the decreased price is calculated using the formula,\[{\text{Decreased Price}} = {\text{Actual Price}} - {\text{Decreased Percentage}} \times {\text{Actual Price}}\].

We will now find the decreased price of the car after \[5\% \] reduction using the above formula.

\[

{\text{Decreased Price}} = 67.6 - \dfrac{5}{{100}} \times 67.6 \\

= 67.6 - \dfrac{{338}}{{100}} \\

= 65 - 3.38 \\

= {\text{Rs. }}61.62 \\

\]

Thus, the decreased price of the care is Rs. \[61.62\].

Therefore, the required price of the car is Rs. \[61.62\].

Note: In solving these types of questions, you should be familiar with the concept of increased price and decreased price. Students should also remember the properties of probability for ease. There is a fair possibility that the student uses the inverse of the formula and will end up getting the wrong answer.

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