Question

Balanced diet should contain $ 12\% $ of proteins, $ 25\% $ of fat and $ 63\% $ of carbohydrates. If a child needs 2600 calories in his food daily, find in calories the amount of each of these in his daily food intake.

Answer 1

Hint: In this question, the value of three diet contents of balanced diet, proteins, fat and carbohydrates are given as their percentage value and we are asked to find the amounts of these contents in terms of calories. As the total calories required for the daily food intake of a child is given, we will find the amount of each content with respect to this total calories.
Formula used:
 $ a\% $ of $ b = \dfrac{{a \times b}}{{100}} $

Complete step-by-step answer:
Here, it is given that the balanced diet should contain $ 12\% $ of proteins, $ 25\% $ of fat and $ 63\% $ of carbohydrates.
Total calories needed by a child in his food daily is given as 2600 calories.
We will take this total calories as $ 100\% $ and find the calories of contents accordingly.
Let us first consider proteins.
Balanced diet should contain $ 12\% $ of proteins. Therefore calories of proteins in balanced diet is $ 12\% $ of the total calories which is calculated as:
 $ \Rightarrow 12\% $ of $ 2600 $ $ = \dfrac{{12 \times 2600}}{{100}} = 312 $
Thus, Child’s daily food should contain 312 calories of protein.
Now, we will calculate fat.
It is given that a balanced diet should contain $ 25\% $ of fat. Therefore calories of fat in balanced diet is $ 25\% $ of the total calories which is calculated as:
 $ \Rightarrow 25\% $ of $ 2600 $ $ = \dfrac{{25 \times 2600}}{{100}} = 650 $
Thus, Child’s daily food should contain 650 calories of fat.
The last content is carbohydrates.
We are given that a balanced diet should contain $ 63\% $ of carbohydrates. Therefore calories of carbohydrates in balanced diet is $ 63\% $ of the total calories which is calculated as:
 $ \Rightarrow 63\% $ of $ 2600 $ $ = \dfrac{{63 \times 2600}}{{100}} = 1638 $
Thus, Child’s daily food should contain 1638 calories of carbohydrates.
Our final answer is: The child’s daily food should contain $312$calories of protein, $650$ calories of fat and $1638$ calories of carbohydrates.

Note: In this type of question, we can check whether our answer is correct or not. For example, here if we add all three content’s amounts in calories, it should be equal to the total calories required for daily food for a child.
Protein calories + fat calories + carbohydrate calories
 $
   = 312 + 650 + 1638 \\
   = 2600 \;
  $
Which is total calories required. Thus, our answer is correct.