Question

One type of liquid contains 20% 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. 20%
B. $$24{\displaystyle \frac{2}{7}}$$ %
C. 37 %
D. 40 %

Answer 1

Hint: First find the parts of water in 10 parts of first liquid by multiplying the given percentage with 10. Next find the parts of water in 4 parts of second liquid by multiplying the given percentage with 4. Then we have to add to get the total part of water in the mixture and then we can find the percentage by dividing it with 14, as the total part in a mixture of first liquid and second liquid is 14 parts.

Complete step-by-step answer:
In the question, we are given that one type of liquid contains 20% 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. So, we have to find the percentage of water in the new mixture in the glass.
Now, we will first find the part of water in 1 part of the first type of liquid. Since, water is 20 %, one part will have $${\displaystyle \frac{20}{100}}=0.2$$ part of water in the first type of liquid. Similarly, in the second part of the liquid it has 35 %, water. So, one part will have $${\displaystyle \frac{35}{100}}=0.35$$ part of water in the second type of liquid.
Now, in a mixture there are 10 parts of the first liquid, so it has $$0.2\times 10=2$$ parts of water. Also, there are 4 parts of second liquid, so it has $$0.35\times 4=1.4$$ parts of water. So, there are total $$2+1.4=3.4$$ parts of water in total $$10+4=14$$ parts of first liquid and second liquid together.
Hence the percentage of water in the new mixture is found as follows:
 $$\begin{array}{rl}& \Rightarrow {\displaystyle \frac{water}{total}}\times 100\mathrm{\%}\\ & \Rightarrow {\displaystyle \frac{3.4}{14}}\times 100\mathrm{\%}\\ & \Rightarrow {\displaystyle \frac{340}{14}}\mathrm{\%}\\ & \Rightarrow 24{\displaystyle \frac{2}{7}}\mathrm{\%}\end{array}$$
Hence, the correct answer is option B $$24{\displaystyle \frac{2}{7}}$$ %

Note: It is important to convert percentages in number. Also, for the final answer we have to find the convert back the number in percentage by multiplying it with 100. So, avoid this common error.