There are two vessels of milk of different prices with the volume of 2

Question

There are two vessels of milk of different prices, per litre, with the volume of 220 litres and 180 litres, respectively. Equal amounts of milk were poured off simultaneously from the two vessels and the milk poured off from the first vessel was poured into the second vessel and milk poured off from the second vessel was poured into the first vessel. Then the price of milk in both the vessels, per litre, becomes the same. How much milk was poured from one vessel into the other?

A. 80
B. 90
C. 99
D. 160
E. Cannot be determined

Are You Up For the Challenge: 700 Level Questions

There are 2 drums of oil of different prices, their volume being 220 gallons and 180 gallons. Equal quantities are drawn off from the 2 drums. The oil drawn from the first drum is poured into the second drum, and the oil drawn from the second drum is poured into the first drum. Then the price of oil per gallon in both drums becomes equal. How much is drawn from each drum?

Divyanshu14 · Accepted Answer

A shortcut method which applies just to questions of this pattern.

Quantity of milk poured: (Volume of vessel 1 * Volume of vessel 2) / (Volume of vessel 1 + Volume of vessel 2)

Here,

Q= 220*180/220+180
 = 99

Cheers!

DrFuManchu1971 · Answer

Price per liter of 220L vessel: A

Price per liter of 180L vessel: B

Amount moved from each vessel: L

Equation:
((220-L)*A + L*B)/220= ((180-L)*B + L*A)/180

Solving it gives you a result of L=99

Answer C

rajatchopra1994 · Answer

Explanation:

Vessel 1 per litre milk price which contains 220L milk = x, total price = 220x
Vessel 2 per litre milk price which contains 180L milk = y, total price = 180y
S Litre milk removed from each vessel
So, Price of vessel 1 = {(220 - S)x + S*y}/ 220
Price of vessel 2 = {(180 - S)y + S*x}/ 180
Price of vessel 1 = Price of vessel 2
{(220 - S)x + S*y}/ 220 = {(180 - S)y + S*x}/ 180
{(220 - S)x + S*y}/11 = {(180 - S)y + S*x}/9
9*(220x - S*x + S*y = 11*(180y - S*y + S*x}
1980x - 9S*x + 9S*y = 1980y - 11S*y + 11S*x
1980*(x-y) = 20(S*x - S*y)
1980 (x - y) = 20S(x - y)
1980 = 20S
S = 99
IMO-C

carouselambra · Answer

I think this is a beautiful question!
However, I tend to have an affinity towards using/plugging numbers to derive an answer instead of algebra.

Can someone please help me with an example of the same?
Thanks in advance!

paragw · Answer

I don't know why no one is using allegation Here's a simple way Let https://gmatclub.com/forum/download/file.php?id=86205 Applying allegation https://gmatclub.com/forum/download/file.php?id=86206 a-P/P-b = x/220-x......eqn 1 a-P/P-b = 180-x/x......eqn2 Equating both the equations, we get x/220-x = 180-x/x x^2 = (220-x)(180-x) only 99 satisfies this equation Hence, C GMAT-Club-Forum-u01596yw.png GMAT-Club-Forum-y4n2avp8.png

There are two vessels of milk of different prices with the volume of 2

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

There are two vessels of milk of different prices with the volume of 2

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