In a class, the number of boys is more than the number of girls by 12% of the total strength. The ratio of boys to girls is

a)15:11 b)11:14 c)14:11 d)8:11

Question

In a class, the number of boys is more than the number of
girls by 12% of the total strength The ratio of boys to girls
is
a)15:11 b)11:14 c)14:11 d)8:11

Aakash Sharma · Accepted Answer

Let the total strength of class be x

Then 12% of total strength $= \frac{12}{100} x = \frac{3}{25} x$

Let the total number of girls be y

Then the number of boys = number of girls + 12% of total strength $= y + \frac{3}{25} x$

Now total strength = number of boys + number of girls

$\Rightarrow x = y + \frac{3}{25} x + y = 2 y + \frac{3}{25} x \Rightarrow 2 y = x - \frac{3}{25} x = \frac{25 x - 3 x}{25} = \frac{22}{25} x \Rightarrow y = \frac{22}{2 \times 25} x = \frac{11}{25} x ....... (1)$

Thus number of boys : Number of girls $= y + \frac{3}{25} x : y$

$= \frac{y + \frac{3}{25} x}{y} = \frac{\frac{11}{25} x + \frac{3}{25} x}{\frac{11}{25} x} (from (1)) = \frac{\frac{14}{25} x}{\frac{11}{25} x} = \frac{14}{11} = 14 : 11$

In a class, the number of boys is more than the number of girls by 12% of the total strength. The ratio of boys to girls is a)15:11 b)11:14 c)14:11 d)8:11

In a class, the number of boys is more than the number of girls by 12% of the total strength. The ratio of boys to girls is

a)15:11 b)11:14 c)14:11 d)8:11