Two vessels a and b contains acid of different concentration. The capacity of a and b are 6 liters and 3 liters respectively. We take out same quantity from both vessels and put into one another, now the concentration in both vessel are same. Find the taken out quantity
Answers
2 litres are emptied from each container and poured into the other
Step-by-step explanation:
A and b are two containers in which 6 liters and 3 litres of same type of acid of different concentrations are kept.
Let say Acid in 1st container = A litre
Water in 1st container = 6 - A litre
x litre emptied Then Acid Removed = Ax/6
Water Removed = (6-A)x/6
Acid in 2nd container = B litre
Water in 2nd Container = 3 - B Litre
x litre emptied Then Acid Removed = Bx/3
Water Removed = (3-B)x/3
now Acid in 1st Container = A - Ax/6 + Bx/3 = (6A - Ax + 2Bx)/6
Axid in 2nd Container = B - Bx/3 + Ax/6 = (6B - 2Bx + Ax)/6
((6A - Ax + 2Bx)/6)/6 = ((6B - 2Bx + Ax)/6)/3
=>6A - Ax + 2Bx = 2(6B - 2Bx + Ax)
=> 6A - Ax + 2Bx = 12B - 4Bx + 2Ax
=> 6Bx - 3Ax = 12B - 6A
=> x(6B - 3A) = 2(6B - 3A)
=> x = 2
2 litres are emptied from each container and poured into the other
taken out quantity = 2 litre from each container
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