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22 May 2020, 07:44
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Difficulty:
35%
(medium)
Question Stats:
76% (02:31) correct
24%
(02:38)
wrong
based on 469
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A subway train made eleven stops on its route. If an average (arithmetic mean) of 30 passengers boarded at each of the first nine stops and at each stop, beginning with the second, 5 fewer passengers boarded than at the previous stop, how many passengers boarded the train at its first stop?
A. 60
B. 50
C. 30
D. 20
E. 10
PS21199
A. 60
B. 50
C. 30
D. 20
E. 10
PS21199
28 May 2020, 16:40
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Bunuel
A subway train made eleven stops on its route. If an average (arithmetic mean) of 30 passengers boarded at each of the first nine stops and at each stop, beginning with the second, 5 fewer passengers boarded than at the previous stop, how many passengers boarded the train at its first stop?
A. 60
B. 50
C. 30
D. 20
E. 10
Since at each stop, beginning with the second, 5 fewer passengers boarded the train than at the previous stop, the number of passengers boarding the train at each of the first nine stops forms an evenly-spaced set. Therefore, the 5th stop must have the median, or the average, number of passengers, which is 30. So, the 4th stop has 35, the third has 40, the second has 45, and finally, the first stop has 50 passengers.A. 60
B. 50
C. 30
D. 20
E. 10
Answer: B
General Discussion
yashikaaggarwal
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22 May 2020, 07:58
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Let the no. Of passengers board the train on first station be {A}, Second be {A-5}, Third {A-10}, fourth {A-15}......... Ninth {A-40}
Average of passengers of first nine stations is 30
Total of passengers/ no. Of stations= average.
Total of passengers= 30*9
{A} + {A-5} + {A-10} + {A-15} + {A-20} +..... + {A-40} = 270
9A-180=270
( 180 = Sn = n/2{2a+(n-1)*d} )
S8 = 8/2{2*5+(8-1)*5} =
S8 = 180. Arithmetic Progression sum )
9A=450
A=50
So 50 passengers board the train.
Answer is B
Posted from my mobile device
Average of passengers of first nine stations is 30
Total of passengers/ no. Of stations= average.
Total of passengers= 30*9
{A} + {A-5} + {A-10} + {A-15} + {A-20} +..... + {A-40} = 270
9A-180=270
( 180 = Sn = n/2{2a+(n-1)*d} )
S8 = 8/2{2*5+(8-1)*5} =
S8 = 180. Arithmetic Progression sum )
9A=450
A=50
So 50 passengers board the train.
Answer is B
Posted from my mobile device
