Question
A barrel contains some wine. A man drank 15 litres from
it and refilled the barrel with same quantity of water so that no one finds out. He did it one more time before someone checked and found the quantity of wine in the barrel to be 48 litres. Find the quantity of wine initially present in the barrel.Solution
We know quantity of wine left is = P × {1 - (R/P)}n {Where 'P' is the initial quantity of wine, 'R' is the quantity withdrawn each time and 'n' is number of times the process is done.} Let the initial quantity of wine in the barrel be 'I' litres. 48 = I × {(I - 15)/I}2 48I = (I – 15)2 48I = I2 – 30I + 225 I2 – 78I + 225 = 0 I2 – 75I – 3I + 225 = 0 I(I – 75) – 3(I – 75) = 0 (I – 3)(I – 75) = 0 I = 75, 3 Since, quantity of wine left in the barrel is 48 litres. So, initial quantity of wine cannot be 3 litres. So, initial quantity of wine in the barrel = 75 litres
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