Proportion Problem Solving

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Let the quantity of sugar solution to be added be x litres.

Setting up the proportion, sugar solution / salt solution = (15 x)/30 = 2/1 → x = 45.

Let us take a look at some examples: Question: In a mixture of 45 litres, the ratio of sugar solution to salt solution is 1:2.

What is the amount of sugar solution to be added if the ratio has to be 2:1?

a, d are called the extremes and b, c are called the means.

For a proportion a:b = c:d, product of means = product of extremes → b*c = a*d.Extra bleach is added to it to make it to 50% bleach solution. So, for each kg of cashews added, let’s consider it as ‘-5’ and for each kg of walnuts added, let’s consider it as ‘ 15’.How much water has to be added further to bring it back to 20% bleach solution? In the first part, there is 20% of bleach in 20 L of solution → 4 L of bleach in 16 L of water = 20 L of solution. These two have to be added in such a way that they cancel out each other.Therefore, 48 litres of water has to be added to the solution if bleach has to be 20% of the whole solution. We know, the first term (1st) and the fourth term (4th) of a proportion are called extreme terms or extremes, and the second term (2nd) and the third term (3rd) are called middle terms or means.Therefore, 5/6 = 20/____To get 20 in the numerator, we have to multiply 5 by 4. 6 by 4Thus, 5/6 = 20/6 × 4 = 20/24Hence, the required numbers is 243. Therefore, 12, x, 8 and 14 are in proportion i.e., 12 : x = 8 : 14⇒ x × 8 = 12 × 14, [Since, the product of the means = the product of the extremes]⇒ x = (12 × 14)/8⇒ x = 21Therefore, the second term to the proportion is 21.The first, third and fourth terms of a proportion are 12, 8 and 14 respectively. Then, 12/100 = x/60 → x = 7.2 ml Therefore, 7.2 ml is present in 60 ml of water. So in order to get a 8% chlorine solution, we need to add 90-60 = 30 ml of water.In order for this 7.2 ml to constitute 8% of the solution, we need to add extra water. Question: There is a 20 litres of a solution which has 20% of bleach.Therefore, 45 litres of sugar solution has to be added to bring it to the ratio 2:1.Question: A certain recipe calls for 3kgs of sugar for every 6 kgs of flour.


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