Question

In school X, the number of boys is more than that of the girls by $40\% $, In the school Y, the number of girls is more than that of boys by $50\% $. If $50\% $ boys in school X is equal to $70\% $of girls is school Y, what is the ratio between the number of students of school X and school Y?
(A)$24:25$
(B)$16:17$
(C)$3:4$
(D)$36:25$

Answer 1

Hint: In this question generally we have to take a value of the variable and we have to add some percentage of the variable to itself as we are given in this question. So to solve this question the general formula that we can write to add a percentage of variable to itself i.e. (variable itself)$ + $percentage(variable). Similar approach will be seen by you in the complete step by step answer.

Complete step by step solution:
In school$X$,
Let number of girls$ = x$
Let number of boys$ = x + \dfrac{{40}}{{100}} \times x$
                                    $\
   = x + \dfrac{{2x}}{5} \\
   = \dfrac{{7x}}{5} \\
 $
Total number of students in school $X$$ = $number of boy’s$ + $number of girls
                                                                      $\
   = x + \dfrac{{7x}}{5} \\
   = \dfrac{{12x}}{5} \\
 $
In school$Y$,
Let number of girls $ = y$
Let number of boys$ = y + \dfrac{{50y}}{{100}}$
                                   $\
   = y + \dfrac{{1y}}{2} \\
   = \dfrac{{3y}}{2} \\
 $

Total number of students in school $Y$$ = $number of boy’s$ + $number of girls
                                                                      $\
   = y + \dfrac{{3y}}{2} \\
   = \dfrac{{5y}}{2} \\
 $
We are also provided with another hint also i.e.
$50\% $of boys in school$X = 70\% $of girls in school $Y$
$50\% $(boy’s in school$X$)$ = $$70\% $( Girls in school $Y$)
$ \Rightarrow $$\dfrac{{50}}{{100}}\left( {\dfrac{{7x}}{5}} \right) = \dfrac{{70}}{{100}}\left( {\dfrac{{3y}}{2}} \right)$
       $\
  \dfrac{1}{2} \times \dfrac{{7x}}{5} = \dfrac{7}{{10}}\left( {\dfrac{{3y}}{2}} \right) \\
  x = \dfrac{{3y}}{2} \\
 $
Total number of students in school $X$$ = \dfrac{{12x}}{5}$
                                                                $ \Rightarrow \dfrac{{12}}{5} \times \dfrac{{3y}}{2}$
                                                                $ = \dfrac{{18y}}{5}$
Total number of students in school $Y = \dfrac{{5y}}{2}$
Ratio of number of students in school $X$ to school $Y$$ = \dfrac{{\dfrac{{18y}}{5}}}{{\dfrac{{5y}}{2}}}$
                                                                                                 $ = 36:25$
 Which is the required answer.
So the correct option is (D).

Note: Interpret the information properly like do not interpret ‘$X$’, ‘$Y$’ as ‘$x$’, ‘$y$’ because the answer will vary as the ratio of ‘$x$’ and ‘$y$’ will be too much varying from total number of students in school ‘$X$’, and school ‘$Y$’.