Question

In a class, there are 64% boys. Had there been 2 more boys and 9 more girls, then boys would have made 62.5% of total students. Find the total number of student in that class.​

Answer 1

Answer:

The total number of students in that class $=325$

Step-by-step explanation:

Let's assume that the total number of students in that class is x.

64% of x are boys.

Therefore, number of boys $=\frac{64x}{100} = \frac{16x}{25}$

Now the scenario with 2 more boys and 9 more girls:

Number of boys in this scenario $= \frac{16x}{25} + 2 = \frac{16x + 50}{25}$

And, total number of students $=x + 2 + 9 = x + 11$

According to the problem:

$\frac{\frac{16x + 50}{25}}{x + 11} = \frac{62.5}{100}$

$=>\frac{16x + 50}{25}= (x + 11)\frac{625}{1000}$

$=>40(16x + 50)= 625(x + 11)$

$=>8(16x + 50)= 125(x + 11)$

$=>128x + 400= 125x + 1375$

$=>3x = 975$

∴ $x = \frac{975}{3} = 325$