Concept:Use the alligation rule to find the proportion in which two mixtures must be combined to achieve a target ratio.
Explanation:First, find the fraction of milk in each mixture.
Mixture 1: milk fraction =
3/(3+2)=3/5.
Mixture 2: milk fraction =
7/(7+3)=7/10.
Target mixture: milk fraction =
5/(5+3)=5/8.
Apply alligation on the milk fractions:
Take the difference between the target and each mixture fraction.
Difference with mixture 1:
3/5−5/8=(24−25)/40=−1/40.
Difference with mixture 2:
5/8−7/10=(50−56)/80=−6/80.
Ignore the negative signs; the required ratio is the absolute values of these differences taken in cross order.
Ratio of mixture 1 to mixture 2 =
806​:401​.
Simplify:
806​=403​, and
401​=401​. So ratio =
3:1.
Answer:The mixtures must be mixed in the ratio
3:1. Option C.