Question

The ratio of the number of boys and girls in a college is 7:8 . If the persentage increase in the number of boys and girls be 20% and 10% . respectively,what will be the new ratio​

Answer 1

Step-by-step explanation:

Originally, let the number of boys and girls in the college be 7x and 8x respectively

Their increased number is (120% of 7x) and (110% of 8x)

$$\eqalign{ & \Rightarrow \left( {\frac{{120}}{{100}} \times 7x} \right)\,{\text{and}}\,\left( {\frac{{110}}{{100}} \times 8x} \right) \cr & \Rightarrow \frac{{42x}}{5}\,{\text{and}}\,\frac{{44x}}{5} \cr & \therefore {\text{The}}\,{\text{required}}\,{\text{ration}} \cr & = \left( {\frac{{42x}}{5}:\frac{{44x}}{5}} \right) \cr & = 21:22 \cr} $$

Answer 2

Answer:

21:22

Step-by-step explanation:

Let's say number of boys = 7k

And number of girls = 8k

Now,

percentage increase in no. of boys = 20%

So, New number of boys = 7k + 20% of 7k

                                          => 7k + (20/100)× 7k

                                           => 7k + 7k/5

                                           => 42k/5

Now, New number of girls = 8k + 10% of 8k

                                          => 8k + (10/100)× 8k

                                           => 8k + 4k/5

                                           => 44k/5

Hence, Ratio = New Number of boys / New Number of girls

                      => (42k/5) / (44k/5)

                        => 42:44 ==> 21:22