Question

If 4 litres of petrol cost Rs. 248, how many litres of petrol can be purchased for Rs. 434?

Answer 1

Hint: We first try to form the proportionality equation for the variables. We take an arbitrary constant. We use the given values of the variables to find the value of the constant. Finally, we put the constant’s value to find the equation.

Complete step-by-step solution:
We have been given the relation between two variables where we assume the number of litres of petrol as r and cost of petrol as t.
The inversely proportional number is actually directly proportional to the inverse of the given number. The relation between r and t is inverse relation.
It’s given r varies directly as t which gives $r\propto t$.
To get rid of the proportionality we use the proportionality constant which gives $r=kt$.
Here, the number k is the proportionality constant. It’s given $r=4$ when $t=248$.
We put the values in the equation $r=kt$ to find the value of k.
So, $4=248k$. Simplifying we get $$k={\displaystyle \frac{4}{248}}={\displaystyle \frac{1}{62}}$$.
Therefore, the equation becomes with the value of k as $r={\displaystyle \frac{t}{62}}$.
Now we simplify the equation to get the value of r for cost being 434
$$r={\displaystyle \frac{434}{62}}=7$$
Therefore, the number of litres of petrol in Rs. 434 is 7.

Note: In a direct proportion, the ratio between matching quantities stays the same if they are divided. They form equivalent fractions. In an indirect (or inverse) proportion, as one quantity increases, the other decreases. In an inverse proportion, the product of the matching quantities stays the same.