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Two solutions having milk and water in the ratios 3 : 5 and 4 : 7 are mixed in the ratio 2 : 3. What is the ratio of milk and water in the resultant mixture?
A. 80 : 139
B. 81 : 139
C. 82 : 139
D. 83 : 139
E. 84 : 139
A. 80 : 139
B. 81 : 139
C. 82 : 139
D. 83 : 139
E. 84 : 139
RamseyGooner
Current Student
Joined: 29 Feb 2020
Last visit: 03 Oct 2022
Posts: 55
Given Kudos: 56
Location: India
Schools: Said '23 (A) Judge '23 (WA) Bocconi (A$$) ESSEC (A)
GMAT 1: 720 Q49 V40
GPA: 3.5
25 May 2021, 00:55
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Oh how much I despise Ratios,
Method1 :
Given Ratios,
3:5 = 8x
4:7 = 11x
Lets bring them to a common stage so that we treat them as lets say liters(as it is milk) andnot ratios
LCM of above is 88, lets multiply 11 at top and 8 at bottom
So, we got : 33:55 and 32:56
First soln is taken twice and the second thrice,
33*2+32*3 : 55*2+56*3 = 162:278
Reduce to get 81:139
However if you are comfortable with ratios, Method 2
Milk in : soln 1 = 3/8, Soln 2 =4/11
Water in : soln 1 =5/8, Soln 2 = 7/11
Soln 1:Soln2 = 2:3
[2(3/8)+3(4/11)]/[2(5/8)+3(7/11)] = 81/139
Hope this helps!
Method1 :
Given Ratios,
3:5 = 8x
4:7 = 11x
Lets bring them to a common stage so that we treat them as lets say liters(as it is milk) andnot ratios
LCM of above is 88, lets multiply 11 at top and 8 at bottom
So, we got : 33:55 and 32:56
First soln is taken twice and the second thrice,
33*2+32*3 : 55*2+56*3 = 162:278
Reduce to get 81:139
However if you are comfortable with ratios, Method 2
Milk in : soln 1 = 3/8, Soln 2 =4/11
Water in : soln 1 =5/8, Soln 2 = 7/11
Soln 1:Soln2 = 2:3
[2(3/8)+3(4/11)]/[2(5/8)+3(7/11)] = 81/139
Hope this helps!
Milk in 1 liter solution —\(\frac{3}{8}\)
Milk in 1 liter solution —\(\frac{4}{11}\)
Milk in 1 liter solution — x
————————————————
\(\frac{4}{11}\) ———x—————\(\frac{3}{8}\)
—> \((x—\frac{4}{11}) / (\frac{3}{8} —x)\) = \(\frac{2}{3}\)
\(3x —\frac{12}{11}= \frac{3}{4} —2x\)
\(5x = \frac{3}{4} + \frac{12}{11}\) =\(\frac{(33+ 48)}{44}= \frac{81}{44}\)
—> \(x = \frac{81}{220}\) -- the ratio of milk to the total mixture
--> \(1 - \frac{81}{220}= \frac{139}{220}\) - the ratio of water to the total mixture
The ratio of milk to water in the resultant mixture = \((\frac{81}{220})/(\frac{139}{220})= \frac{81}{139}\)
The answer is B.
Posted from my mobile device
Milk in 1 liter solution —\(\frac{4}{11}\)
Milk in 1 liter solution — x
————————————————
\(\frac{4}{11}\) ———x—————\(\frac{3}{8}\)
—> \((x—\frac{4}{11}) / (\frac{3}{8} —x)\) = \(\frac{2}{3}\)
\(3x —\frac{12}{11}= \frac{3}{4} —2x\)
\(5x = \frac{3}{4} + \frac{12}{11}\) =\(\frac{(33+ 48)}{44}= \frac{81}{44}\)
—> \(x = \frac{81}{220}\) -- the ratio of milk to the total mixture
--> \(1 - \frac{81}{220}= \frac{139}{220}\) - the ratio of water to the total mixture
The ratio of milk to water in the resultant mixture = \((\frac{81}{220})/(\frac{139}{220})= \frac{81}{139}\)
The answer is B.
Posted from my mobile device
