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Directions: Study the following table chart carefully and answer the questions given:

The table chart below shows the percent of boys and the total students in all the colleges.

 Colleges P Q R S Years % of Boys Total Students % of Boys Total Students % of Boys Total Students % of Boys Total students 2011 60 240 45 300 30 200 36 150 2012 75 280 30 250 60 260 40 200 2013 50 220 40 320 45 240 210 2014 50 230 35 280 45 340 55 240 2015 50 290 260 320 60 300 2016 55 340 35 220 35 240 40 280
Important for :
1
What is the total number of girls studying in all the colleges together in the year 2013, if we assume the total percent of boys in college S for the year 2013 as 80% of the percentage of the boys of college P in 2013?
» Explain it
B
First of all, we need to find the percentage of boys in college S = 80% of 50% of total = 40% of total

Now, we can make the table as follows:

 Colleges P Q R S Years % of Boys Total Students % of Boys Total Students % of Boys Total Students % of Boys Total students 2011 60 240 45 300 30 200 36 150 2012 75 280 30 250 60 260 40 200 2013 50 220 40 320 45 240 40 210 2014 50 230 35 280 45 340 55 240 2015 50 290 45 260 45 320 60 300 2016 55 340 35 220 35 240 40 280

From the table,

Total number of girls in the year 2013 = (50% of 220 + 60% of 320 + 55% of 240 + 60% of 210)

= (110 + 192 + 132 + 126) = 560
Hence, option B is correct.
2
What is the respective ratio of girls studying in all colleges in the year 2015 to the year 2016, if the sum of all percentages of boys in 2015 is 200% and college Q and college R have the same percentage of boys?
» Explain it
E
First, we need to find the percent of boys in Q and R

Total percentage of boys = 200%

So, Q + R = 200% – (50 + 60)% = 90%

Hence, Q & R will get 45% each.

 Colleges P Q R S Years % of Boys Total Students % of Boys Total Students % of Boys Total Students % of Boys Total students 2011 60 240 45 300 30 200 36 150 2012 75 280 30 250 60 260 40 200 2013 50 220 40 320 45 240 210 2014 50 230 35 280 45 340 55 240 2015 50 290 45 260 45 320 60 300 2016 55 340 35 220 35 240 40 280
From the above table,

Total number of girls studying in the year 2015 = (50% of 290 + 55% of 260 + 55% of 320 + 40% of 300)

= (145 + 143 + 176 + 120) = 584

Similary, in 2016 = (45% of 340 + 65% of 220 + 65% of 240 + 60% of 280)

= (153 + 143 + 156 + 168) = 620

∴  Required ratio = 584 : 620 = 146 : 155

Hence, option E is correct.

3
What is the difference between the total number of boys studying in all the colleges together in the year 2012 and the total boys studying in all the colleges together in the year 2014?
» Explain it
B
From the given table,

The total number of boys studying in the year 2012 = (75% of 280 + 30% of 250 + 60% of 260 + 40% of 200)

= (210 + 75 + 156 + 80) = 521

Similary, in the 2014 = (50% of 230 + 35% 280 + 45% of 340 + 55% of 240)

= (115 + 98 + 153 + 132) = 498

∴   Required difference = 521 – 498 = 23

Hence, option B is correct.

4
What is the approximate average number of girls studying in all the colleges together in the year 2011?
» Explain it
A
From the given table,

Total number girls studying in the year 2011 = (40% of 240 + 55% of 300 + 70% of 200 + 64% of 150)

= 96 + 165 + 140 + 96 = 497

 ∴   Average number of boys = 497 = 124.25 ≈ 124 4

Hence, option A is correct.

5
With reference to college Q, the total number of boys is approximately what percent of the total number of students over the years, if missing percentage value is equal to the percent of boys in 2014 in college R.
» Explain it
B
By considering missing element equal to the % of boys in college R in 2014, we get

 Colleges P Q R S Years % of Boys Total Students % of Boys Total Students % of Boys Total Students % of Boys Total students 2011 60 240 45 300 30 200 36 150 2012 75 280 30 250 60 260 40 200 2013 50 220 40 320 45 240 210 2014 50 230 35 280 45 340 55 240 2015 50 290 45 260 320 60 300 2016 55 340 35 220 35 240 40 280

From the above table,

Total number of students in college Q over the years = (300 + 250 + 320 + 280 + 260 + 220) = 1630

And the total number boys in college Q over the years = (45% of 300 + 30% of 250 + 40% of 320 + 35% of 280 + 45% of 260 + 35% of 220)

= (135 + 75 + 128 + 98 + 117 + 77) = 630
 ∴   Reqd % = 630 × 100 = 38.65 ≈ 39% 1630

Hence, option B is correct.