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There were N stations on a railroad. After adding X stations
46 additional tickets have to be printed.
Find N and X.
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Answer Posted / guest
Let before adding X stations, total number of tickets
t = N(N-1)
After adding X stations total number of tickets are
t + 46 = (N+X)(N+X-1)
Subtracting 1st from 2nd
46 = (N+X)(N+X-1) - N(N-1)
46 = N2 + NX - N + NX + X2 - X - N2 + N
46 = 2NX + X2 - X
46 = (2N - 1)X + X2
X2 + (2N - 1)X - 46 = 0
Now there are only two possible factors of 46. They are
(46,1) and (23,2)
Case I: (46,1)
2N - 1 = 45
2N = 46
N = 23
And X = 1
Case II: (23,2)
2N - 1 = 21
2N = 22
N = 11
And X = 2
Hence, there are 2 possible answers.
| Is This Answer Correct ? | 33 Yes | 4 No |
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