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The ratio of boarders to day scholars at a school is 7 to 16. However,

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The ratio of boarders to day scholars at a school is 7 to 16. However,  [#permalink]

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New post 24 May 2015, 06:25
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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

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Re: The ratio of boarders to day scholars at a school is 7 to 16. However,  [#permalink]

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New post 24 May 2015, 09:03
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The question is needlessly confusing, partly because of the grammar (the first sentence needs to say 'was', not 'is', since the 7 to 16 ratio is the situation in the past, before the new boarders arrive).

Regardless, we have a 7 to 16 ratio initially, of boarders to day scholars. We then add some boarders, while the scholars remain the same, and the ratio becomes 8 to 16 (multiplying the 1 to 2 ratio by 8). So the initial number of boarders increases by 1/7, and the answer is (1/7)(560) = 80.

Or you can proceed algebraically - if the ratio is 7 to 16, and we have 560 boarders, then our 'multiplier' is 80, so we have 80*16 = 1280 day scholars initially, and 1840 students in total. If we then add k boarders, we have 560+k boarders and 1280 day scholars. If these are in a 1 to 2 ratio, then we have

2(560 + k) = 1280
1120 + 2k = 1280
2k = 160
k = 80
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Re: The ratio of boarders to day scholars at a school is 7 to 16. However,  [#permalink]

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New post 25 Jun 2017, 09:57
Boarders/Day Scholars = 7/16

No. of boarders initially = 560, so, number of day scholars initially = 560*16/7 = 1280.

Let the no. of new boarders be x, so, Boarders + x/Day scholars = 1/2. Since the number of day scholars remained the same, the value of x works out to - 1280/2 - 560 = 80. Ans - D.
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Re: The ratio of boarders to day scholars at a school is 7 to 16. However,  [#permalink]

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New post 09 Mar 2018, 16:04
Hi All,

This is actually a mid-level ratio question, since you're given so much information to work with. You can also do the "ratio math" in a variety of different ways.

The ratio of Boarders to Day-scholars is 7:16 and we're told that there are 560 boarders. This means….

B : D
7 : 16
560 : 1280

We're told that new boarders enter the school; this changes the ratio to…

B : D
1 : 2

Since the number of Day-scholars is "locked" at 1280, we just need to add Boarders until we get to half of 1280…

560 + X = 640
X = 80

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Re: The ratio of boarders to day scholars at a school is 7 to 16. However,  [#permalink]

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New post 03 Oct 2018, 10:08
oarders/Day Scholars = 7/16

No. of boarders initially = 560, so, number of day scholars initially = 560*16/7 = 1280.

We're told that new boarders enter the school; this changes the ratio to…

B : D
1 : 2

Since the number of Day-scholars is fixed at 1280, we just need to add Boarders until we get to half of 1280…

560 + X = 640
X = 80
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Re: The ratio of boarders to day scholars at a school is 7 to 16. However,   [#permalink] 03 Oct 2018, 10:08
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