Ratio word problems

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Ratio is a very basic and common concept in mathematics. Ratio is the comparison between quantitates or numbers. The symbol for the representing ratio is “:”. Ratio helps in solving questions related to comparisons, proportions and many word problems.  For example, a / b can be written as a : b. Here a / b is fraction form and a:b is the ratio form. The ratio can be simplifies if a and b have any common factors. 

Example 1: In the drawing class there are 5 girls and 6 boys. In the singing class there are 7 girls and 6 boys. Which class had higher girls to boy ratio?
Solution: The ratio between number of boys and number of girls in the drawing class = 5: 6.
The ratio between number of boys and number of girls in the singing class = 7: 6.
Comparing both the ratio’s writing in the fraction form: 5/6 and 7/6.
Here the denominator of the fractions is the same so the fraction with grater numerator is greater.
Hence, 7/6 > 5/6.
Therefore the ratio between the number of girls and boys is greater in the singing class.
 
Question: Multiple choice question (Pick the correct option.)
What is equivalent ration to 24: 12?
a)    1: 2                 b) 2: 1                        c) 1:3              d) None of these.
Correct answer: option b.
Explanation: The given ratio can be further simplified as 24 and 12 have a common factor 12.
                                    Therefore, dividing 24 and 12 by 12 gives 24: 12 = 2: 1.

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