Instructions

Study the following information and answer the question:

In a college, there are 2400 students who are enrolled in any one of the five branches of engineering A, B, C, D and E. The ratio of the number of boys to that of girls is 7:5. 15% of the boys and 22% of the girls are enrolled in A. $$\frac{2}{7}$$ of the number of boys are enrolled in B. A total of 500 boys are enrolled in D and E and the ratio of the number of boys in D and that in E is 2 : 3. The remaining boys are enrolled in C.

26% of the total number of girls are enrolled in D and 120 girls enrolled in B. The number of girls enrolled in C is 100 more than the number of girls in E.

Question 54

# The total number of girls enrolled in B and E is what percent less than the total number of boys enrolled in A and C?

Solution

We know that the ratio of the total number of Boys to Girls ratio is 7:5;
we also know that the total number of students is 2400.
Taking Boys and Girls to be 7x and 5x respectively, we get 12x = 2400, giving us x = 200
And hence, the total number of boys to be 1400 and the total number of girls to be 1000.

Next we're given that 15% of the boys are in section A, $$\frac{15}{100}\times\ 1400=210$$
And 22% of the girls are in section B, $$\frac{22}{100}\times\ 1000=220$$

Next, $$\frac{2}{7}$$ of the boys are in section B, $$\frac{2}{7}\times\ 1400\ =\ 400$$

We are also given that 500 boys are split between D and E in the ratio of 2:3, which would mean that D has 200 boys and E has 300 boys.
And the remaining boys are in Section C; the number of boys remaining are 290.

Next, we are given that 26% of the girls are in section D, that would mean that section d has 260 girls.
We are also given that section B has 120 girls.

The remaining girls must be split between section C and E, of which we know that C has 100 girls more than section E.
Taking the number of girls in section E to be x, we can calulculate these values as we know that 400 girls are yet to be place in any section,
giving us the equation $$2x+100=400$$
or simply $$x=150$$
which means that section E has 150 girls and Section C has 250 girls.

Our final data looks like this:
SectionÂ  BoysÂ  Girls
A
Â  Â  Â  Â  Â  Â  Â 210Â  220
BÂ  Â  Â  Â  Â  Â Â
400Â  120
CÂ  Â  Â  Â  Â  Â Â
290Â  250
DÂ  Â  Â  Â  Â  Â Â
200Â  260
EÂ  Â  Â  Â  Â  Â Â
300Â  150

Total number of Girls in B & E =Â $$120+150=270$$
Total number of Boys in A & C =Â $$210+290=500$$

Ratio of the C&E girls to A&C boys isÂ $$\frac{270}{500}=\ 0.54$$
Which means that there are 46% less girls in C&E than the boys in A&C.

Therefore, Option B is the correct answer.Â