Alligations or Mixtures

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A can contains a mixture of two liquids A and B in the ratio 7:5 when 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially?


28 litres


21 litres


45 litres


36 litres

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Option(B) is correct

Suppose the can initially contains $7x$ and $5x$ litres of mixtures A and B respectively.

When 9 litres of mixture are drawn off, quantity of A in mixture left:

$7x-\left(\dfrac{7}{12}\right)\times 9 = 7x -\dfrac{21}{4}$ litres
Similarly quantity of B in mixture left:
$5x-\left(\dfrac{5}{12}\right)\times 9 = 5x -\dfrac{15}{4}$ litres

Therefore ratio becomes:
\Rightarrow \dfrac{28x-21}{20x+21}&=\dfrac{7}{9}\\
\Rightarrow 252x-189&=140x+147\\
\Rightarrow 112x &=336\\
\Rightarrow x&=3
So the can contained:  
$7\times x=7\times 3= 21$ litres of A initially.

(4) Comment(s)


I think initial mixture should be, $7+5=12\times 3=36$

Sreethi Reddy

what abt addition of b??

Mangesh Kumar

what about addition of b


Mangesh, I think the when the ratio becomes $7:9$, there is a typo in the solution.

the $3^{rd}$ equation given should be modified from:
\(\dfrac{7x-(21/4)}{5x-(15/4)}=\dfrac{7}{9}\) to
\(\dfrac{7x-(21/4)}{5x-(15/4)+ \textbf{9}}=\dfrac{7}{9}\)

Which will take us to the correct next step as given in the existing solution.

I guess they will take it into consideration and and update the solution.