In what ratio should a 20% methyl alcohol solution be mixed with a 50%

Question

In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?

A. 1 : 3
B. 1 : 2
C. 2 : 3
D. 2 : 1
E. 3 : 1

generis · Accepted Answer

To find the ratio of two solutions in a resultant mixture, weighted average works well. I use this formula: 
  (Concen_{A})(Vol_{A}) + (Concen_{B})(Vol_{B} = (Concen_{A+B})(Vol_{A+B})

Let A = volume of the solution with 20 percent alcohol

Let B = volume the solution with 50 percent alcohol

A + B = resultant mixture

(.20)(A) + (.50)(B) = .40(A + B) ==>

(20)(A) + (50)(B) = 40(A + B)

20A + 50B = 40A + 40B

10B = 20A

Ratio is either  \frac{A}{B} , or  \frac{B}{A} . Be careful about order. The prompt asks for the ratio of the 20 percent solution to the 50 percent solution, that is, for the ratio of A to B.

10B = 20A

\frac{10}{20}  =  \frac{A}{B}

A:B is 1:2

ANSWER B

chetan2u · Answer

Hi,

TWO things to remember:- 
 1) the ratio of quantity mixed to get an average is related to the ratio of each qty's distance from average.
2) More the Qty of x from that of y, More CLOSER will be average to x..

Qty of 20%/Qty of 50%=  \frac{(50-40)}{(40-20)}=\frac{1}{2}= 1:2 
B

Senthil7 · Answer

Hi chetan, i did not understand that as the explanation was too technical. Can you or someother expert please simplify?

gracie · Answer

.2x+.5y=.4(x+y)
x/y=1/2=1:2

chetan2u · Answer

Hi,
the Q is-
In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?

Now one solution is 20% and other is 50%, and the mix has an average of 40%..... 
Now had both 20% and 50% been equal, the average would be \frac{20+50}{2}= 35 %. But the average is 40%, which is even further closer to 50%, so the quantity of 50% should be MORE than 20%...

HOW much?  it is equal to the RATIO of distance from the average.. 
 This is weighted average method... 
QTY of 20%/QTY of 50% = Distance of average from 50%/ distance of average from 20% =  \frac{50-40}{40-20} = \frac{1}{2} ..

so Qty of 20%/Qty of 50% = 1/2......

abhinabhishek · Answer

equation will be
(.20x+.50y)/(x+y)=.40 where x &y mixture used for 20% m.a.s and 50% m.a.s volumes
On solving we get
2x=1y
X/y=1/2

Posted from my mobile device

Abhishek009 · Answer

MA _______________________________ EA

20 _______________________________ 50
 _______________ 40 __________________
 10 _______________________________ 20

Using rule of Alligations, Answer must be (B) 1 : 1

Archit3110 · Answer

solve using allegation method
20 50
 40 
10 20
10:20 ; 1:2
IMO B

RahulKhanna77 · Answer

PLEASE USE THE SCALE METHOD POSTED BY BUNUEL

Kinshook · Answer

In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it?

20% 50%

40%

50%-40%=10% 40%-20%=20%

10%:20% = 1:2

Ratio = (50%-40%): (40%-20%) = 1:2

IMO B

In what ratio should a 20% methyl alcohol solution be mixed with a 50%

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In what ratio should a 20% methyl alcohol solution be mixed with a 50%

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards