At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?
A. 4
B. 6
C. 9
D. 12
E. 15
OA: 4
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cook / waiter = 3/13 and cook / waiter + 12 = 3/16GmatKiss wrote:At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?
A. 4
B. 6
C. 9
D. 12
E. 15
OA: 4
solve it waiter, you endup 52 and cooks 12.
Hence D!
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GMATGuruNY
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Here's an efficient non-algebraic approach:GmatKiss wrote:At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?
A. 4
B. 6
C. 9
D. 12
E. 15
OA: 4
The original ratio of cooks to waiters = 3:13, so the original number of waiters is a multiple of 13:
13,26,39,52,65...
When 12 waiters are added, the new ratio = 3:16, so the increased number of waiters is a multiple of 16:
16,32,48,64,80...
The values in red are 12 apart.
Thus, the original number of waiters = 52.
Since 3:13 = 12:52, the original number of cooks = 12.
The correct answer is D.
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Abhishek009
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Cooks to the number of waiters is 3 to 13GmatKiss wrote:At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?
A. 4
B. 6
C. 9
D. 12
E. 15
OA: 4
c/w = 3a/13a { Let a be the common factor }
When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16
So , 3a/(13a + 12 ) = 3/16
So, 48a = 39a + 36
Or , 9a = 36
So , a = 4
We know , c/w = 3a/13a
So total number of cooks is 3*4 => 12
Abhishek
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HeyArnold
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Use the unknown variable here, since it's a ratio...
Cooks: 3x
Waiters: 13x
so if you add 12 waiters then...
3x / (13x + 12) = 3 / 16
Cross multiply
3(13x + 12) = 3x(16)
39x + 36 = 48x
36 = 9x
x = 4, plugging back into 3x = 3(4) = 12
Answer is [spoiler]D
[/spoiler]
Cooks: 3x
Waiters: 13x
so if you add 12 waiters then...
3x / (13x + 12) = 3 / 16
Cross multiply
3(13x + 12) = 3x(16)
39x + 36 = 48x
36 = 9x
x = 4, plugging back into 3x = 3(4) = 12
Answer is [spoiler]D
[/spoiler]
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saketk
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C/w = 3/13GmatKiss wrote:At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?
A. 4
B. 6
C. 9
D. 12
E. 15
OA: 4
this means C = 3x and W= 13x
now the new count of W = 13x+12
the corresponding ratio is
3x/(13x+12) = (3/16)
48x = 39x+36
this gives x= 4
So the number of Cooks = 4*3 = 12
Option D
