Question : A school group charters three identical buses and occupies $\frac{4}{5}$ of the seats. After $\frac{1}{4}$ of the passengers leave, the remaining passengers use only two of the buses. The fraction of the seats on two buses that are now occupied is:
Option 1: $\frac{8}{9}$
Option 2: $\frac{7}{10}$
Option 3: $\frac{7}{9}$
Option 4: $\frac{9}{10}$
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Correct Answer: $\frac{9}{10}$
Solution :
Let the number of seats in each bus be $x$.
According to the question,
The total number of seats in the three buses is $3 × x = 3x$.
Total passengers = $3x × \frac{4}{5} =\frac{12x}{5}$.
$\frac{1}{4}$ of the total passengers leave the bus.
Remaining passengers = $\frac{12x}{5}\times\frac{3}{4}=\frac{36x}{20}$
So, the fraction of the seats on the two buses that are now occupied is:
$\frac{36x}{20}\times\frac{1}{2x}=\frac{9}{10}$
Hence, the correct answer is $\frac{9}{10}$.
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