Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk. If the vessel now contains water and milk in the ratio 9:40. Find the capacity of the vessel?
A. 14litres
B. 24litres
C. 16litres
D. 12litres
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Option checking method: Taking Option A
First replacement:
After 8 liters of water are removed, the remaining water = 14-8 = 6 liters.
After 8 liters of milk are added, the amount of milk = 8 liters.
Removal of 8 more liters:
Since 8/14 = 4/7, the amount of water and the amount of milk each decrease by 4/7, implying that 3/7 of each volume remains.
Thus:
Remaining water = (3/7)6 = 18/7 liters.
Remaining milk = (3/7)8 = 24/7 liters.
Second replacement:
After 8 liters of milk are added, the total volume of milk = 24/7 + 8 = 80/7 liters.
Resulting ratio of water to milk:
W:M = (18/7) : (80/7) = 18:80 = 9:40.