General solution for mixture problems.
In this type of problems S1 consisting of some components and S2 consisting of one or more of the same components are mixed
Steps:
1.Identify the S1 and S2 and their components. For simplicity let us assume S1 and S2 are solutions. They may also be solids such as bars.
2.S1 and S2 are identified as follows:
(i)S1 and S2 are explicitly mentioned as two different solutions.
(ii)S1 is the original solution. S2 is the same type of solution but added to S1. The elements become added in the proportion they are present
(iii)S1 is the original solution and S2 is a different type of solution and may contain only one element ,such as water. This element will be present in S1 also.
(iv)S1 is the original solution and S2 is the same type of solution got from removing some quantity from S1. The elements are removed in the same proportion they are present.
(v)S1 is the original solution and S2 is that which is got by removing only one element from S1.
(vi)S1 and S2 are two solutions and they contain only one element or only one element is mentioned.
3.The general formula is:
re1/re2 = s1 *e1/(e1+e2) + s2* e1/(e1+e2) / s1*e2/(e1+e2) + s2* e2/(e1+e2)
where re1/re2 is the ratio of the elements in the result after s1 and s2 are mixed, s1 and s2 are the quantity of the solutions . The elements in each solution are normally given in ratios.
In this problem,
re1/re2 = 10/100 * s1 + 30/100*s2 / 90/100 *s1 + 70/100 * s2
re1/re2 = 0.1*s1 + 0.3 *s2 / 0.9*s1 + 0.7*s2
25/75= 0.1*s1 + 0.3 *s2 / 0.9*s1 + 0.7*s2
=> s1/s2 = 1/3 or s1/(s1+s2) = 1/4
The answer is therefore 25%
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