srfn wrote:The ratio of boarders to day scholars at a school is 7 to 16. However, after a few new students join the initial 560 boarders, the ratio changed to 1 to 2, respectively. If no boarders became day scholars and vice versa, and no students left the school, how many boarders joined the school?
A) 48
B) 64
C) 70
D) 80
E) 84
Let b = borders and d = day scholars.
Original ratio:
Here, b/d = 7/16.
Since the actual value of b is 560, and 7*80 = 560, the multiplier for the ratio is 80:
b/d = (80*7)/(80*16) = 560/1280.
Thus:
b=560, d=1280, total number of students = 560+1280 = 1840.
New ratio:
Here, b/d = 1/2.
Thus, of every 3 students, 1 is a boarder and 2 are day scholars, implying that the 1280 day scholars must be equal to 2/3 of the new total:
1280 = (2/3)x
x = 1920.
Thus, after the new boarders join the school, the new total number of students = 1920.
Thus:
New boarders = (new total) - (old total) = 1920 - 1840 = 80.
The correct answer is
D.
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. Thanks for clearing it up, hopefully this question and explanation will be useful to some.
