Lots Of Adulteration :o
A barrel is completely filled with water. 27 litres of water is removed from it and an equal quantity of milk is added. It is stirred properly and 27 litres of the mixture is removed. An equal quantity of milk is again added so that the barrel is still completely full. Now, if the milk and water in the barrel are found to be in the ratio 9:16, find the capacity of the barrel (in litres).
The answer is 135.
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1 solution
Let V be the capacity of the barrel. (All capacities in litres)
After the first step, Water remaining = V-27 Milk = 27
On removal, Water removed = 27 × (V-27)/V Milk removed = 27 × (27/V)
After second removal, Water remaining = (V-27) - 27×(V-27)/V Milk remaining = 27 - 27×(27/V)
Finally, Water in barrel = The same value as above. Milk in barrel = The value after second removal + 27
Ratio of milk : water = 9:16 Solving, we get (V-15)(V-135)=0
V obviously cannot be 15
Therefore 135 is the result we are left with :)