A vessel contains a mixture of milk and water in the respective ratio of 14 : 3. 25.5 litres of the mixture is taken out from the vessel an… — Answer & Discussion

A vessel contains a mixture of milk and water in the respective ratio of 14 : 3. 25.5 litres of the mixture is taken out from the vessel and 2.5 litres of pure water and 5 litres of pure milk is added to the mixture. If the resultant mixture contains 20% water, what was the initial quantity of mixture in the vessel before the replacement? (in litres)

A51
B102
C68
D85

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Discussion 1

CCommunity21 May 2019

Solution
Let the total quantity of mixture in the vessel initially = $17x$ litres
=> Quantity of milk = $\frac{14}{17} \times 17x = 14x$ litres
Quantity of water = $17x - 14x = 3x$ litres
Acc. to ques,
=> $\frac{14x - (\frac{14}{17} \times 25.5) + 5}{3x - (\frac{3}{17} \times 25.5) + 2.5} = \frac{80}{20}$
=> $\frac{14x - 21 + 5}{3x - 4.5 + 2.5} = \frac{4}{1}$
=> $\frac{14x - 16}{3x - 2} = \frac{4}{1}$
=> $14x - 16 = 12x - 8$
=> $14x - 12x = 16 - 8$
=> $x = \frac{8}{2} = 4$
$\therefore$ Initial quantity of mixture in the vessel before the replacement = $17 \times 4 = 68$ litres