Question

One type of liquid contains 20% of water, and the second type of liquid contains 35% of water. A glass is filled with 10 parts of the first liquid and 4 parts of the second liquid. The percentage of water in the new mixture in the glass is:
(a) 37%
(b) $\dfrac{170}{7}\%$
(c) 40%
(d) 20%

Answer 1

Hint: It is a word problem related to percentages and ratio, and the only thing that you need to focus on for solving this problem is the percentage calculation. To start, let the amounts of the two types of liquids be the variables. Then use the conditions given in the question to form equations and use the method of substitution to solve the problem.

Complete step-by-step answer:
To start with the solution, let us let the amount of liquid of type 1 in the mixture be x litre and of type 2 be y litre.
Now, calculating the amount of water in the mixture due to the presence of liquid of type 1 is:
Water content from type 1 $\text{=}\left( \text{amount of type 1} \right)\times \dfrac{\text{percentage of water}}{100}$
\[\Rightarrow \text{water content from type 1=x}\times \dfrac{20}{100}=\dfrac{x}{5}\text{ litre}\]
Similarly, calculating the amount of water in the mixture due to the presence of liquid of type 2 is:
Water content from type 2 $\text{=}\left( \text{amount of type 2} \right)\times \dfrac{\text{percentage of water}}{100}$
\[\Rightarrow \text{water content from type 2=y}\times \dfrac{30}{100}=\dfrac{7y}{20}\text{ }litre\]
Also, it is given that $\dfrac{x}{y}=\dfrac{10}{4}$
$\Rightarrow x=\dfrac{5y}{2}.............(i)$
Now the percentage of water content in the mixture can be calculated as below.
Percentage of water in the new mixture $\text{=}\dfrac{\text{sum of water contents of both types}}{\text{total amount of mixture}}\times 100$
$\Rightarrow \text{percentage of water in the new mixture=}\dfrac{\dfrac{x}{5}+\dfrac{7y}{20}}{x+y}\times 100$
Now we will substitute the value of x from equation (i) in our equation. On doing so, we get
Percentage of water in the new mixture $\text{=}\dfrac{\dfrac{5y}{5\times 2}+\dfrac{7y}{20}}{\dfrac{5y}{2}+y}\times 100=\dfrac{17y}{7y}\times 10=\dfrac{170}{7}\%$
Therefore, the answer to the above question is option (b).

Note: Try to keep your equations as clean as possible by removing the unwanted terms to reduce the chances of making calculation and sign related mistakes. Make sure that you are using all the data given in the question wisely, else you might not reach the final answer.