Question

The bus and train fare between two cities is in the ratio 3:4. If the bus fare increases by 10% and the train fare increases by 20%. Which of the following is the ratio of the new fares?

• A. 11:16
• B. 7:9
• C. 7:8
• D. 22:36

Answer 1

The correct option is A 11:16

Let the original bus and train fares be 3x and 4x, respectively.

As the bus fare increases by 10%, the new bus fare is:

$3x+3x\times \left(\frac{10}{100}\right)=3x+0.3x=3.3x=\frac{33x}{10}$

And the train fare increases by 20%, the new fare is:

$4x+4x\times \left(\frac{20}{100}\right)=4x+0.8x=4.8x=\frac{48x}{10}$

Hence, the new ratio of bus and train fares
$=\left(\frac{33x}{10}\right)$ : $\left(\frac{48x}{10}\right)=33:48=11:16$