Question

A chocolate contains 55 percent sugar, 20 percent cocoa and the rest is butter and milk. The mass of chocolate is 150 grams. Find the mass of sugar and cocoa in the chocolate.

Answer 1

Hint: Now we know that total mass of chocolate bar is 150 grams. Now the percentage is sugar is given to be 55 percent. Hence the weight of sugar used in chocolate is 50 percent of 150 grams. Similarly, the weight of cocoa in the chocolate is 20 percent of 150 grams.

Complete step-by-step solution:
Let us understand the percentage. Firstly the percentage is nothing but a fraction with denominator. Hence when we say 50 percent what we have is $\dfrac{50}{100}$. Now let us see what this means. The fraction says 50 parts out of 100. Hence when we say there is 50 percent of sugar we mean for every 100 grams it contains 50 grams of sugar.
Now we are given that chocolate consist of 55 percent sugar and 20 percent cocoa and the weight of chocolate is 150 grams.
Now let us first calculate the mass of sugar added in the chocolate.
Now since there is 55 percent sugar we can say that out of every 100 grams, 55 grams is sugar
Hence for 1 gram, we have $\dfrac{55}{100}$ grams of sugar.
Hence for 150 grams, we have $\dfrac{55}{100}\times 150$ grams of sugar.
$\dfrac{55}{100}\times 150=82.5$
Hence 150 grams of chocolate have 82.5 grams of sugar.
Now let us calculate the mass of cocoa.
Now since there is 20 percent cocoa we can say that out of every 100 grams, 20 grams is cocoa.
Hence we have for, 1 gram of chocolate $\dfrac{20}{100}$ grams is cocoa
Hence, for 150 grams of chocolate
     \[\dfrac{20}{100}\times 150\]
 grams is cocoa
Now $\dfrac{20}{100}\times 150=30$
Hence we have 30 grams of cocoa in 150 grams of chocolate.

Note: One should note that these types of questions are needed to be solved by the unitary method. The unitary method states that first calculate the value of 1 unit and then calculate the value of the desired unit.\[\]