Question

The number of boys is more than the number of girls by 12% of the total strength of the class. The ratio of the number of boys to that of girls is:
A. \[11{\rm{ }}:{\rm{ }}14\]
B. \[14{\rm{ }}:{\rm{ }}11\]
C. \[25{\rm{ }}:{\rm{ }}28\]
D. \[28{\rm{ }}:{\rm{ }}25\]

Answer 1

Hint: A ratio shows the relative sizes of two or more values.

Complete step by step solution:
Let total number of students = $100$
\[B + G = 100\].........(1)
According to the question, the number of boys is more than the number of girls by \[12\% \] of the total strength.
We have taken the total strength as \[100\].
Writing it in equation form, we’ll get
\[B = G + 12\% 100\]B=G+12÷100×100
\[B = G + 12\]
From equation (1)
\[G + 12 + G = 100\]
\[2G + 12 = 100\]
\[2G = 100 - 12\]2G=88
\[G = 44\]
Again, from equation (1)

B/G = 56/44
B:G = 14:11

Therefore, option B is correct.

Additional information: The percent value is computed by multiplying the numeric value of the ratio by \[100\]. For example, to find \[50\]apples as a percentage of \[1250\]apples, one first computes the ratio \[50/1250\; = {\rm{ }}0.04\], and then multiplies by \[100\]to obtain \[4\% \].The percent value can also be found by multiplying first instead of later, so in this example, the \[50\]would be multiplied by \[100\]to give \[5,000\], and this result would be divided by \[1250\] to give \[4\% \].
To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, \[50\% {\rm{ }}of{\rm{ }}40\% \]is:
\[50/100\; \times \;40/100\; = {\rm{ }}0.50{\rm{ }} \times {\rm{ }}0.40{\rm{ }} = {\rm{ }}0.20{\rm{ }} = \;20/100\; = {\rm{ }}20\% .\]
It is not correct to divide by \[100\]and use the percent sign at the same time. For example, \[25\% {\rm{ }} = \;25/100\; = {\rm{ }}0.25\], not \[25\% /100\], which actually is ​\[^{25}{ / _{100}}/100\; = {\rm{ }}0.0025\]. A term such as \[100/100\% \;\]would also be incorrect, since it would be read as \[1\] percent, even if the intent was to say \[100\% \].
Whenever communicating about a percentage, it is important to specify what it is relative to (i.e., what is the total that corresponds to \[100\% \]).


Note:
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100, which means, a part per hundred. The word percent means per 100. It represented by the symbol “%”. If we say, 50% of a number, then it means 50 percent of its whole.