SRCC GBO 2023 Question Paper

Profit percentage of B in 2018 is 45%, 
Using the given formula for profit percentage and the given expenditure, we can find the income of B in 2018
$$\frac{Income-300}{300}=\frac{45}{100}$$
$$Income\ =\ 135+300=435\ crores$$
The profit by B in 2018 is $$435-300=135\ crores$$

Profit percentage of A in 2015 is 30%
Using the given formula for profit percentage and the given income, we can find the expenditure of A in 2015
$$\frac{390-Expenditure}{Expenditure}=\frac{30}{100}$$
$$3900-10Expenditure\ =\ 3Expenditure$$
$$Expenditure=300$$
The profit by A in 2015 is $$390-300=90$$

The ratio of B's profit to A's profit is $$\frac{135}{90}=\frac{3}{2}$$
Which means that B's profit is 150% of A's profit or B's profit is 50% more than A's profit. 

Hence, Option B is the correct answer. 

Let the expenditure of A and B in 2020 be X and 2X respectively, where X is a constant. 
We can see that the profit percent of A in 2020 is 35%
using the formula given for the profit percentage, we get $$\frac{I_A-X}{X}=0.35$$  {$$I_A$$ is the investment made by A}
= $$100I_A-100X=35X$$
=$$I_A=1.35X$$

We can also see that the profit percent of B in 2020 is 55%
Using the formula given for the profit percentage, we get $$\frac{I_B-2X}{2X}=0.55$$  {$$I_B$$ is the investment made by B}
$$10I_B-20X=11X$$
= $$I_B=3.1X$$

Total investment by A and B is 4.45X, which we know is equal to 534 crores, through this we get the value of X to be 120.
Thus, the total investment is 3X, which is $$3\times\ 120=360$$ crores

Therefore, option D is the correct answer. 

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

The difference between the boys enrolled in C and girls enrolled in Section E is
=$$290-150$$
= 140

Hence, Option B is the correct answer. 

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

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

Therefore, Option B is the correct answer. 

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 and girls in section D is $$200+260=460$$
Total number of girls in A, C and E is $$220+250+150=620$$

The required percentage would be $$\frac{460}{620}\times\ 100=74.19$$%
Correcting this to one decimal place would give us 74.2%

Therefore, option A is the correct answer. 

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. 

Export of A in 2015, 2016, 2019 are 
$$320\times\ 0.35=112$$
$$350\times\ 0.30=105$$
$$450\times\ 0.34=153$$
Total : 370

Export of B from 2016 to 2019:
$$200\times\ 0.42=84$$
$$350\times\ 0.34=119$$
$$320\times\ 0.30=96$$
$$300\times\ 0.27=81$$
Total : 308

Their ratio = $$\frac{370}{380}=37:38$$

Hence, Option A is the correct answer. 

B's average production in 2016, 2017 and 2018 is $$\frac{200+350+320}{3}=\frac{870}{3}=290$$
C's Domestic produce in 2015 and 2019 = $$350\times\ \frac{70}{100}(=245)$$ and $$325\times\ \frac{60}{100}(=195)$$
=$$440$$

The required percentage is $$\frac{290}{440}\times\ 100=65.9\%$$
The closest approximation go this would be 66% and hence, option c. 

A's export in 2017 = $$300\times\ \frac{40}{100}=120$$
A's export in 2018 = $$400\times\ \frac{45}{100}=180$$
A's total export in 2017 + 2018 = 300

B's domestic production in 2017 = $$350\times\ \frac{66}{100}=231$$
B's domestic production in 2019 = $$300\times\ \frac{73}{100}=219$$
B's total domestic produce in 2017 + 2019 = 450

A's export is 150 million tonnes less than the B's domestic produce. 
The percentage required  = $$\frac{150}{450}\times\ 100=33.33\%$$

Therefore, option C is the correct answer.