Question

A bus left with some definite no. of passengers. At 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?

Answer 1

Let no. of passengers be $x$

at first stop, no of passengers left and boarded are $\frac{x}{2},35$

no of passengers after first stop will be $x_1=x-\frac{x}{2}+35=\frac{x}{2}+35$

at second stop, no of passengers left and boarded are $\frac{x_1}{5},40$

no of passengers after second stop will be $\left(x_1\right)-\frac{x_1}{5}+40=\frac{4x_1}{5}+40$

given 80 passengers are remaining after second stop,

so $\frac{4x_1}{5}+40=80\Rightarrow \frac{4x_1}{5}=40\Rightarrow x_1=50\frac{x}{2}+35=50\Rightarrow \frac{x}{2}=15\Rightarrow x=30$

no fo passengers boarded at first is $30$