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A bus travelled from station A to station E. There were 45 passengers on the bus when it left station A. At station B, some passengers boarded the bus but no passenger alighted from it. At station C, half of the passengers in the bus alighted and 20 passengers boarded it. Finally at station D, another half of the passengers in the bus alighted and 30 passengers boarded it. There were 80 passengers on the bus as it left station D for station E. How many passengers boarded the bus at station B?

Apr 12, 2023

#1
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26 passengers boarded the bus at station B.

Apr 12, 2023
#2
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At station A

There were 45 passengers on the bus when it left station A

At station B, some passengers boarded the bus but no passenger alighted from it.

Let , number of passengers boarded at B = x

at B no of passenger = 45 + x

At station C, half of the passengers in the bus alighted and 20 passengers boarded it.

at C = $${45 + x \over 2} + 20$$

Finally at station D, another half of the passengers in the bus alighted and 30 passengers boarded it (45 + x)/2 + 20)/2 + 30

There were 80 passengers on the bus as it left station D for station E.

(45 + x)/2 + 20)/2 + 30 = 80
(45 + x)/2 + 20)/2 = 50

(x + 45)/2 + 20 = 100

(x + 45)/2 = 80

x + 45 = 160

x = 115

number of passengers boarded at B = x = 115

Apr 13, 2023