ritula wrote:

To make lemonade, a recipe requires 4 lemons, 30 ounces of sugar, and 2 pints of water. One can squeeze out 0.4 cups of 5% citric acid from an average lemon. Marta does not have lemons, but wants to make lemonade from 4 cups of 12% citric acid. She has sugar and water in abundance. How much water will Marta use?

(A) 2 pt.

(B) 6 pt.

(C) 12 pt.

(D) 15 pt.

(E) 100 pt.

I think Answer should be 17.6 cups : Here is my solution :

One lemon contains 0.4 cups juice concentration 5% acid and 95% of residue liquid (water).

Thus \(Acid = \frac{5}{100} * 0.4 --- and --- residue-liquid (water) = \frac{95}{100} * 0.4\)

Acid = 0.02 cups

Residual (water) = 0.38 cups

4 lemons contains.

Acid = 0.08

Residual (water) = 1.52

4 cups of Citric acid concentrate contains 12% Citric acid and 88% Residual (water)

Thus \(Acid = \frac{12}{100} * 4 --- and --- residue-liquid (water) = \frac{88}{100} * 4\)

Acid = 0.48 cups

residue liquid (water) = 3.52 cups

To calculate number of lemons which contain equivalent citric acid.

\(No- of- Lemons = \frac{0.48}{0.02} = 24\)

\(residue-liquid-(water)- in- 24- lemons = 0.38 * 24 = 9.12\)

residue liquid (water) available from 4 cups of Citric acid is 3.52 cups , but 24 lemons provide 0.38 * 24 = 9.12 cups. Thus in Lemonade we will have to add 9.12-3.52 cups to balance the missing residue liquid (water)

\(9.12 - 3.52 = 5.6 cups\)

Using 4 cups of 12% Citric acid we can make 24/4 = 6 servings of lemonade.

\(Water- required -as- per- the- ratio- provided = 2 * 6 + 5.6 missing- residue- liquid-(water) = 12 + 5.6 = 17.6 (cups- of- water)\)

If we do not add this 5.6 cups of liquid water Martha will get highly concentrated Citric lemonade. Further as ratios are not given in Citric : sugar : water instead given as lemon : sugar : water we must consider to add missing residue else in final mixture fraction of Citric will be higher compared to other ingredient and final ratio wont be same as provide in recipe.

_________________

Piyush K

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