Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and

Solution:

Let the CP of two vodkas be Rs 100 and Rs 100x
and individual profit in Rs on them being A and B.
=> (A+2B)/3 = 10/100*(100+200x)/3
and
(2A+B)/3 = 20/100*(200 + 100x)/3.

solving we get A = (70+20x)/3 and B = (20x-20)/3
=> profit percentages on each is (70+20x)/3 and (20x-20)/3x.

When they are increased to 4/3 and 5/3 times respectively and mixed in the ratio 1:1 we get
total profit % as (4/3*100*(70+20x)/3 + 5/3*100x*(20x-20)/3x)/(100+100x) = 100*(20x+20)/(100+100x) = 20

=> choice (b) is the right answer.

I did not do any calculation on this one.

There are two ingredients in V1 and V2 and we know from the stem that the first ingredient is expensive than the second.

Case I - V1 profit is 10% when mix is 1:2 => profit from second ingredient is more
Case II - V2 profit is 20% when mix is 2:1 => profit from first ingredient is more. Decreasing the first ingredient results in less profit - Case I. Hence first ingredient is more expensive.

If V1 and V2 are mixed in equal ratio then the profit will be closer to 20%. Even though we have equal quantity of each ingredient but first ingredient is more expensive.

Now the trick. When the profit on V1 is increased by 4/3 and V2 is increased by 5/3. This is equivalent to increasing the quantity of V2 as 1.33 < 1.67. It means the weighted mean will move even closer to 20%

Hence the final mean will be almost 20.

Your logic is right but when options are as close as 20 and 21 its not safe to assume 20.

Only if it were 20, 30 , 40 then its safe to assume 20.

Hi Bunuel,

I am not quite familiar with the allegation formula amit2k9 has used to solve this problem. Could you please show a simpler way of solving this problem?

Thanks,
Ishan

Thanks Bunuel for this explanation. It's quite clear this way. Kudos!

Hi Bunuel, When we say Increased By -- Don't we add the values i.e. previous + current... in this case if the profit increased by 4/3 times the previous value shouldn't we add 40 + 30.. i.e. increased by 40% means 70%..

If the question had been increased to 4/3 times then we could have taken 40% i.e. from 30% it has changed to 40%.

Please help!!!!

Hi Bunuel,
I got your method except how you got 30%. Will you explain, please, how you have solved and got 30%?
Thanks in advance.

We have x+ 2y = 30 and 2x+y = 60

Multiplying 2nd equation by 2, we can say

2*( 2x+y = 60) = 4x +2y=120

Now subtract the 1st equation from this new equation, we will have

4x + 2y=120
- x + 2y=30
---------------------
3x = 90
or x=30.

I Hope its clear now.

The wording of the question is off and is not at all GMAT-like.

When V1 and V2 are mixed in ratio 1:2, avg profit = 10%
1/2 = (P2 - 10)/(10 - P1)

When V1 an dV2 are mixed in ratio 2:3, avg profit = 20%
2/1 = (P2 - 20)/(20 - P1)

Cross multiply to get P1= 30 and P2 = 0

when P1 is increased to 40 and P2 to 0 (note that we are assuming that it becomes 4/3 not increases by 4/3), and the vodkas are mixed in the ratio 1:1,

1/1 = (0 - P)/(P - 40)
P = 20

Answer (B)

The question says profit increased by 4/3 and 5/3 times which means 7/6x and 8/6x. It seems like the question language is incorrect