Answer:
- 15 years old
- 45 liters of sugar solution
Explanation:
You have ages in the ratio 3:5:7, with the average age being 25, and you want to know the age of the youngest. You have 45 L of a solution in the ratio sugar : salt = 1 : 2, and you want to know how much sugar solution to add to make the ratio 2 : 1.
Ages
The age ratios are an arithmetic progression with an odd number of terms, so the middle one is the average. That is, the average age of 25 years corresponds to 5 ratio units. Then the youngest boy is ...
3/5 × 25 = 15 . . . . years old
Solution
The ratio 1 : 2 of sugar solution to salt solution tells you that the fraction that is sugar is 1/(1+2) = 1/3 of the whole amount, or ...
sugar solution = 1/3 · 45 L = 15 L
Then the salt solution is ...
salt solution = 45 L -15 L = 30 L . . . . . . . or (2/3·45 L)
To make the solution have twice as much sugar solution as salt solution, we need a total of 2·(30 L) = 60 L of sugar solution. We already have 15 L, so we need to add ...
added sugar solution = 60 L -15 L = 45 L
45 L of sugar solution must be added to make the sugar : salt ratio be 2 : 1.
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Additional comment
The "solution" problem can also be worked by considering "ratio units." The original sugar:salt ratio is 1:2. To make it be 2:1 while keeping the salt constant, we need to increase the ratio from 1:2 to 4:2. That is, we need to add 4-1 = 3 units of sugar solution. The 45 L amount is the amount of 1+2=3 units of solution, so we need to add 45 L of sugar solution.