Question

The bus fare between two cities is increased in the ratio 7:9. Find the increase in the fare, if:
(1) the original fare is Rs 245
(2) the increased fare is Rs 207

Answer 1

Hint: Here, we will assume the increased fare to be equal to x in case (1). Then, we will equate the ratio of the original fare and increased fare to the given ratio, that is, 7: 9. Similarly, in the second case, we will assume the original fare to be y and then we will equate the ratio of the original fare and increased fare to 7:9. In this way, we can find the values of x and y. The difference between the increased fare and original fare will give the increase in fare.

Complete step-by-step answer:
(1) Let us assume that the increased fare is = x.
Since, it is given that the fare is increased in the ratio 7:9. So, we can write:
$\dfrac{\text{original fare}}{\text{increased fare}}=\dfrac{7}{9}$
$\begin{align}
  & \Rightarrow \dfrac{245}{x}=\dfrac{7}{9} \\
 & \Rightarrow 245\times 9=7\times x \\
 & \Rightarrow x=\dfrac{245\times 9}{7} \\
 & \Rightarrow x=35\times 9=315 \\
\end{align}$
So, the value of x comes out to be 315. Therefore, the increased fare is Rs 315.
We have to increase the fare which means that we will have to calculate the difference between the increased fare and original fare.
So, increase in fare = Rs 315 – Rs 245 = Rs 70
Hence, the increase in fare is = Rs 70.

(2)
Let us assume that the original fare is equal to y.
Since, the fare is increased in the ratio 7:9, we can write:
$\dfrac{\text{original fare}}{\text{increased fare}}=\dfrac{7}{9}$
$\Rightarrow \dfrac{y}{207}=\dfrac{7}{9}$
$\begin{align}
  & \Rightarrow y\times 9=7\times 207 \\
 & \Rightarrow y=\dfrac{1449}{9}=161 \\
\end{align}$
So, the value of y comes out to be 161 which means that the original fare is Rs 161.
Increase in fare = Increased fare – original fare = Rs 207 – Rs 161 = Rs 46.
Hence, the increase in fare is = Rs 46.


Note: Students should note here that the ratio of original fare to increased fare is 7:9. A wrong interpretation may lead to wrong results. One probability of mistake is that students might get confused while finding the increase in fare, whether they subtract the original fare from increased fare or vice versa. But here we have to always subtract the original from the increased fare otherwise we will get a negative result which is wrong.