SRCC GBO 2023 Question Paper

School     Total      Passed      Distinction      Without distinction     Failed
A             800            640             300                       340                       160
B            1050           840              350                       490                      210
C            1200           920              450                       470                      280
D             750            600              260                       340                      150
E             900            750              330                        420                     150
F            1500          1000             450                        550                     500


Using our collected data, we can easily calculate the average number of students who failed in A, B, C and E to be $$(160+210+280+150)/4=800/4=200$$
The number of students who passed without distinction is 340.

Ratio of these two values is $$\frac{200}{340}=0.588$$
Which means that the average number of students who failed in A, B, C and E is 41.176% smaller than the number of students who passed without distinction in D. 
This is approximately 41%. 

Therefore, Option A is the correct answer. 

School   Total   Passed   Distinction    Without distinction      Failed
A             800          640          300                    340                         160
B            1050         840           350                    490                         210
C            1200         920           450                    470                         280
D              750         600           260                    340                         150
E              900         750           330                    420                          150
F             1500        1000         450                     550                         500


We are given that the 840 students who passed in B, the boy to girl ratio is 3:4, which gives us 360 boys and 480 girls in B.
Similarly, we are given that of the 920 students who passed in C, the boy to girl ratio is 11:12, which gives us 440 boys and 480 girls in C. 
And now we can calculate the total number of boys who passed from B and C, 800 boys. 

Next. the total number of students who passed with distinction from D, E and F are $$260+330+450=1040$$

the ratio of these students to the boys from B&C is $$\frac{1040}{800}=1.3$$
Which tells us that there are 30% more students who passed with distinction from D,E and F when compared to the number of boys from B&C. 

Therefore, Option B is the correct answer.  

Upon calculating the number of vacant seats on every day of the week, we get the data. 

The total number of seats vacant throughout the week would be 630. 

In making a pie chart, these 630 seats would encompass 360 degrees. So the number of degrees per seat would be $$\frac{360}{630}$$
Monday will have $$\frac{360}{630}\times\ 105\ =\ 60$$ degrees
Thursday will have $$\frac{360}{630}\times\ 140\ =\ 80$$ degrees

The difference between the angles covered by Monday and Thursday will be 20 degrees. 

Hence, Option D is the correct answer. 

Calculating the 2nd class non-Ac vacant seat data and Wednesday's  vacant seat data, we get 

Calculating the 2nd Non-AC vacant seats on Monday, Tuesday and Friday we get, $$210+180+150=540$$
Vacant seats on Wednesday are, $$60+120+140+125+35=480$$

The ratio of Wednesday vacant seats to 2nd Non-AC seats is 0.888 or 88.88%
This means that there are 11.11% less seats. 

Therefore, option A is correct. 

Calculating the vacant seats in AC Tier I class, gives us the data

Average number of reserved seats in 2nd Class Non-Ac on Wednesday and Saturday is $$\frac{\left(840+760\right)}{2}=800$$
Total number of vacant seats in AC I tier are $$50+30+35+25+20+12=172$$

The required percentage is $$\frac{172}{800}\times\ 100=21.5\%$$

Therefore, Option A is the correct answer. 

Calculating vacant seats on Thursday and AC III gives us the data, 

Total Vacant seats on Thursday are: $$100+40+80+140+25=385$$
Total vacant seats in AC III are: $$160+90+140+80+150+120=740$$
The difference between them; $$740-385=355$$

Total reserved seats in Non-Ac on Thursday and Saturday are; $$800+360+760+320=2240$$

The required percentage is $$\frac{355}{2240}\times\ 100\approx\ 15.8\%$$

Therefore, Option B is the correct answer. 

Checking the Export for all of the options we see:
Option A: 2017
Wheat Export - 40% of 180 = 72
Rice Export - 28% of 200 = 56
Total Export - 128

Option B: 2019
Wheat Export - 35% of 320 = 112
Rice Export - 48% of 300 = 144
Total Export - 256

Option C: 2020
Wheat Export - 30% of 360 = 108
Rice Export - 40% of 280 = 112
Total Export - 220

Option D: 2018
Wheat Export - 45% of 240 = 108
Rice Export - 32% of 250 = 80
Total Export - 188

As we can see, only option C satisfies our condition.
Therefore, Option C is the correct answer.

Total Domestic consumption of Rice in 2017: 72% of 200 = 144
Total Domestic consumption of Rice in 2019: 52% of 300 = 156
Adding them up we get,  300 million tonnes.

Exports of wheat in 2016, 2017 and 2020 are
$$\left(32\%\ of\ 250\right)+\left(40\%\ of\ 180\right)+\left(30\%\ of\ 360\right)$$
= $$80+72+108$$
= $$260\ $$ million tonnes

Calculating the domestic rice consumption to the wheat export we get, $$\frac{300}{260}=\ 1.1538$$
Which means the domestic consumption is 15.38% higher. 
Rounding it to one decimal place gives us, 15.4%
Hence, option C is the correct answer.  

Domestic consumption of rice in 2019: $$0.52\times\ 300\ =\ 156$$ million tonnes.

Average production of wheat in 2017, 2018 and 2020 is:
$$\frac{\left(180+240+360\right)}{3}=\ \frac{780}{3}=260$$ million tonnes.

Domestic consumption of rice in 2019 as a percentage of average production of wheat in 2017, 2018 and 2020 is $$\frac{156}{260}=0.6$$;
Which is equivalent to 60%

Therefore, Option D is the correct answer. 

Increase of Wheat production from 2019 to 2020: $$\frac{36-32}{32}\times\ 100=12.5\%$$
Wheat production in 2021: $$360\times\ 1.125$$ = 405
The domestic consumption would be $$60\%\ of\ 405$$

Rice production in 2021: $$280\times\ \frac{6}{5}=336$$
Domestic consumption would be $$60\%\ of\ 336$$

The difference between them would be :
= $$60\%\ of\ 405$$ - $$60\%\ of\ 336$$
=$$\frac{3}{5}\times\ \left(405-336\right)=\frac{3}{5}\times\ 69=\frac{207}{5}=41.4$$

Therefore, Option A is the correct answer.