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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.
The difference between the total number of boys enrolled in B and C and the total number of girls enrolled in A and D is x. The total number of boys and girls enrolled in E is y. The x is what percent less than y? (Nearest to an integer)
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:
Section Boys Girls
A 210 220
B 400 120
C 290 250
D 200 260
E 300 150
Total number of boys in B&C = $$400+290=690$$
Total number of girls in A&D = $$220+260=480$$
The difference is x=$$690-480=210$$
Total number of boys and girls in E, y=$$300+150=450$$
The difference between x and y is $$450-210=240$$
This is $$\frac{240}{450}\times\ 100\ =\ 53.33\ \%\ $$ of y.
Rounding it to the nearest integer gives us that x is 53% smaller than y.
Therefore, Option D would be the correct answer.
