Question

Ram prepares solutions of alcohol in water according to customers needs. This morning Ram has prepared 27 litres of a 12% alcohol solution and kept it ready in a 27 litre delivery container to be shipped to the customer. Just before delivery, he finds out that the customer had asked for 27 litres of 21% alcohol solution. To prepare what the customer wants, Ram replaces a portion of 12% solution by 39% solution. How many litres of 12% solution is replaced?

• A. 5
• B. 9
• C. 10
• D. 12

Answer 1

The correct option is B 9

Using alligation we get,

So, ratio of 12% solution to 39% should be 18:9 to get the mixture of required composition.
Hence, solution to be replaced to get the required mixture = $\frac{9}{18+9}\times 27=9litres.$


Alternative Approach:
Let Ram replaces x litres of 12% sol. with 39% solution
Now, quantity of 12% sol. in 27 litre $=\frac{27\times 12}{100}$
$\therefore$ After replacing we have volume of alcohol.
$=(\frac{12\times 27}{100}-\frac{12x}{100}+\frac{39x}{100})=\frac{324+27x}{100}$
this will be equal to 27 litre of 21% sol.
$\therefore \frac{324+27x}{100}=\frac{21\times 27}{100}$
$\therefore x=\frac{567-324}{27}=\frac{243}{27}=9$
Hence option (b)