Alligations or Mixtures
Aptitude

 Back to Questions
Q.

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?

 A.

28 litres

 B.

21 litres

 C.

45 litres

 D.

36 litres

 Hide Ans

Solution:
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:
\begin{align*}
\dfrac{7x-\dfrac{21}{4}}{5x-\dfrac{15}{4}+9}&=\dfrac{7}{9}\\
\Rightarrow \dfrac{28x-21}{20x+21}&=\dfrac{7}{9}\\
\Rightarrow 252x-189&=140x+147\\
\Rightarrow 112x &=336\\
\Rightarrow x&=3
\end{align*}
So the can contained:  
$7\times x=7\times 3= 21$ litres of A initially.


(4) Comment(s)


Elamurugan
 ()

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


Deepak
 ()

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.