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A bus left with some definite no. of passengers. At the first stop half the passengers left the bus and 35 boarded the bus. At the second stop, one-fifth 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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50

20

30

None of these

answer is C.

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Detailed Solution

Let the number of passengers =

x

From the question we have,
The number of passengers left and boarded at first stop are

\frac{x}{2}, 35

Number of passengers after first stop (

x_{1}) = x - \frac{x}{2} + 35 = \frac{x}{2} + 35

The number of passengers left and boarded at second stop are

\frac{x_{1}}{5}, 40

respectively.
Number of passengers after second stop

= x_{1} - \frac{x_{1}}{5} + 40 = \frac{4 x_{1}}{5} + 40

According to question,

\frac{4 x_{1}}{5} + 40 = 80

\Rightarrow \frac{4 x_{1}}{5} = 40

\Rightarrow x_{1} = 50

Since,

\frac{x}{2} + 35 = 50

\Rightarrow \frac{x}{2} = 15 \Rightarrow x = 30

Hence, the number of passengers was originally 30.
.

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