A bus left with some definite number of passengers. At the first stop, half of the passengers left the bus and 35 boarded the bus. At the second stop 1/5 of the passengers left and 40 boarded the bus. Then, the bus moved with 80 passengers towards its destination without stopping anywhere. How many passengers were there originally?

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answer is B.

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Detailed Solution

Suppose there were F passengers initially

Number of passengers after first stop

Number of passengers after second stop

$\begin{matrix} = \frac{4}{5} (\frac{F}{2} + 35) + 40 = 80 \\ \Rightarrow \frac{F}{2} + 35 = \frac{(80 - 40)}{4} \times 5 \\ \Rightarrow \frac{F}{2} = 50 - 35 = 15 \\ F = 30 \end{matrix}$

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