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Study the following table carefully and answer the given questions.

Year State P State Q
Number of appeared candidates Percentage of appeared candidates who qualified Number of appeared candidates Percentage of appeared candidates who qualified
2006 450 60% 30%
2007 600 43% 45%
2008 60% 280 60%
2009 480 70% 550 50%
2010 380 400

Note: Few values are missing in the able (indicated by – ). A candidate is expected to calculate the missing value, if it is required to answer the given question on the basis of the given information.

Important for :
1
Out of the number of qualifies candidates from State P in 2008, the ratio of male to female candidates is 11 : 7. If the number of female qualified candidates from State P in 2008 is 126, what is the number of appeared candidates (both male and female) from State P in 2008?
» Explain it
E
Given ratio of qualified male and female from State P in 2008 is 11 : 7.

Let the total number of qualified students = x. 

  7x    =  126
11 + 7
⇒      x    =   126 × 18   =  324.
7

Let the total number of appeared candidates be y.

Then y × 60% = 324

∴   y =  324 × 100  = 540.
60


Hence, option E is correct.

2
The number of appeared candidates from State Q increased by 100% from 2006 to 2007. If the total number of qualified candidates from State Q in 2006 and 2007 together is 408, what is the number of appeared candidates from State Q in 2006?
» Explain it
C
Let the number of appeared candidates from State Q in 2006 be x.

Then, the number of appeared candidates in 2007 

=   x +  100 × x  
100
=   2x

According to the question,

x × 30  +  2x × 45  = 408
100 100

⇒    3x  +  9x  = 408
10 10
⇒   12x = 4080
⇒       x = 340.

Hence, the number of candidates from State Q in 2006 is 340.

Hence, option C is correct.

3
What is the difference between the number of qualified candidates from State P in 2006 and that in 2007?
» Explain it
A

As per the question, we get

60% of 450 – 43% of 600


Required Difference

=    60 × 450  –  43 × 600  
100 100

= 270 – 258 = 12.


Hence, option A is correct.

4
If the average number of qualified candidates from State Q in 2008, 2009 and 2010 is 210, what is the number of qualified candidates from State Q in 2010?
» Explain it
D
Let the percentage of candidates who qualify from State Q in 2010 be x%

Then,

Average

=    60% of 280 + 50% of 550 + x% of 400      
3
=   210

⇒   168 + 275 + 4x = 630
⇒   4x = 630 – 443 = 187
⇒   x =  187  = 46.75%.
4

∴   Qualified candidates from State Q in 2010 = 46.75% of 400 = 187.

Hence, option D is correct.

5
If the ratio of the number of qualified candidates from State P in 2009 to that in 2010 is 14 : 9, what is the number of qualified candidates from State P in 2010?
» Explain it
C
The ratio of qualified candidates from State P 2009 to that in 2010 is 14 : 9.


Now, in 2009 the number of qualified candidates
=    480 × 70  
100
= 336


Let the number of qualified candidates from State P in 2009 be 14x and in 2010 be 9x. Then,

⇒ 14x = 336 ⇒ x = 24

In 2010 the number of qualified candidates
=   9 × 24
=   216.

Hence, option C is correct.


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