Let us assume price per liter of the mentha oil in container A and B be a and b respectively
From the given information we can say that quantity of oil in the container A and B will be 140 and 60 each respectively; However, concentration or mix/composition will change to achieve an average price which will be between a and b with more aligned towards content of A as A is higher in quantity i.e 140 compared to 60
Average price of the mix = \(\frac{140*a + 60*b}{ 200}\) Equation ---1 which will be equal to the average price of the content in each container
Say x Ltr of oil is drawn from each container and put in the other one
Average price of content of container A = \(\frac{(140-x)*a + x*b }{140}\) Equation ---2
Average price of content of container A = \(\frac{(60-x)*b + x*a}{ 60}\) Equation----3
Equation 1 and 2 and 3 will be equal
From 2 and 3
\(\frac{140*a + x*(b-a) }{ 140} = \frac{60*b + x*(a-b) }{ 60}\)
Solving further ... \(3*14(a-b) = x*(a-b) \)
Since we are given a is not equal to b; a-b can not be zero
x= 3*14 =42
(D) is the answer IMO
Bunuel wrote:
There are two containers A and B filled with mentha oil with different prices and with volumes 140 and 60 liters respectively. Equal quantities are drawn from both A and B in such a manner that the oil drawn from A is poured in into B and oil drawn from B is poured into A. After doing so, the price per liter becomes equal in both containers. What is the (equal) quantity that was drawn?
A. 21 liters
B. 27 liters
C. 35 liters
D. 42 liters
E. 45 liters