Question

Two brands of detergents are to be combined. Detergents A contains 40% bleach and 60% soap. While detergent B contains 25% bleach and 75% soap. If the combined mixture is to be 35% bleach. What % of the final mixture should be detergent A?

Answer 1

Hint: We start solving the problem by assuming the percentages of detergent A and B present in the final mixture as x% and $\left( 100-x \right)\%$ . We then multiply these assumed percentages with the percentages of bleach present in each detergent and add them together. We equate this sum with the percentage of bleach in the final mixture. We then make the necessary calculations to get the required percentage.

Complete step-by-step answer:
According to the problem, we have two brands of detergents to be combined. Detergents A contains 40% bleach and 60% soap. While detergent B contains 25% bleach and 75% soap. We need to find the % of detergent A in the mixture of both detergents if the combined mixture contains 35% bleach.
Let us assume that the final mixture contains x% of detergent A, then it contains $\left( 100-x \right)\%$ of detergent B.
According to the problem, we are given that the final mixture contains 35% bleach.
So, we have $\dfrac{\left( x\times 40 \right)+\left( \left( 100-x \right)\times 25 \right)}{100}=35$.
$\Rightarrow \left( x\times 40 \right)+\left( \left( 100-x \right)\times 25 \right)=\left( 35\times 100 \right)$
$\Rightarrow 40x+2500-25x=3500$.
$\Rightarrow 15x=1000$.
$\Rightarrow x=66.67\%$.
So, we have found that the final mixture contains 66.67% of detergent A.

Note: We can also solve this problem by assuming that the percentages A and B as x% and y% and equating the percentages of bleach and soap in the mixtures to get the percentage of A in the final mixture. We can also find the percentage of detergent B in the final mixture by subtracting the percentage of A from 100%. Similarly, we can expect problems to find the percentage of soap present in the final mixture.