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How many passengers?

A bus stopped at Ryde. Half the passengers got off and 8 new passengers got on. At the next stop, 1/3 of the passengers got off and 4 got on. And at the next stop, 1/5 of the passengers got off and 5 new passengers got on. The bus then had 21 passengers. How many passengers did the bus have just before it stopped at Ryde?
 

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Muhammad C. | Muhammad the grand math tutorMuhammad the grand math tutor
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The bus had 32 passengerat before it stopped at Ryde.

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You have to start from the end & work backwards with this problem. 
 
There were 21 passengers after 5 got on the bus. Before they got on, there were 21 - 5 or 16 passengers. Before those 5 got one, 1/5 of passengers got off. This means 4/5 stayed on which denotes:
 
4/5 * x = 16
 
x = 20
 
Before this, 4 got on after 1/3 got off.
 
20 - 4 = 16
 
2/3 * y = 16
 
y = 24
 
Before this, 8 passengers got on after 1/2 got off
 
24 - 8 = 16
 
1/2 * z = 16
 
z = 32