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Difficulty:
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Question Stats:
50% (03:01) correct
50%
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wrong
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Everyone in Donhill lives either to the east or to the west of the river. Since the turn of the century, the number of residents who live to the east of the river has fallen by 60 percent, whereas the number of residents who live to the west of the river has risen by 540 percent. If the population of Donhill is now 240% of what it was at the turn of the century, what fraction of the residents live to the east of the river?
A. \(\frac19\)
B. \(\frac18\)
C. \(\frac29\)
D. \(\frac14\)
E. \(\frac13\)
A. \(\frac19\)
B. \(\frac18\)
C. \(\frac29\)
D. \(\frac14\)
E. \(\frac13\)
ankushsambare
Joined: 13 Jun 2022
Last visit: 02 Sep 2026
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Location: India
Schools: ISB '27 Wharton '26 INSEAD Aug '26
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18 May 2026, 20:49
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Let initial population = 100
Let east = E, west = W
So:
E + W = 100
East fell 60% → new east = 40% of E = 0.4E
West rose 540% → new west = 640% of W = 6.4W
Current total = 240 →
0.4E + 6.4W = 240
Substitute E = 100 − W:
0.4(100 − W) + 6.4W = 240
40 − 0.4W + 6.4W = 240
40 + 6W = 240
6W = 200
W = 100/3
So:
E = 200/3
Current east:
0.4E = 0.4 × 200/3 = 80/3
Current total = 240
Fraction east:
(80/3) / 240 = 80 / 720 = 1/9
Final Answer: A (1/9)
Let east = E, west = W
So:
E + W = 100
East fell 60% → new east = 40% of E = 0.4E
West rose 540% → new west = 640% of W = 6.4W
Current total = 240 →
0.4E + 6.4W = 240
Substitute E = 100 − W:
0.4(100 − W) + 6.4W = 240
40 − 0.4W + 6.4W = 240
40 + 6W = 240
6W = 200
W = 100/3
So:
E = 200/3
Current east:
0.4E = 0.4 × 200/3 = 80/3
Current total = 240
Fraction east:
(80/3) / 240 = 80 / 720 = 1/9
Final Answer: A (1/9)
19 May 2026, 08:10
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