Directions (46-50): Study the 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 table (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.
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?
380
360
340
320
300
Solution
Let the number of appeared candidates from State Q in 2006 be $x$.
Then, the number of appeared candidates in 2007
$= x + \dfrac{x \times 100}{100} = 2x$
According to the question, $\dfrac{x\times 30}{100} + \dfrac{2x\times 45}{100} = 408$
or, $\dfrac{3x}{10}+\dfrac{9x}{10} = 408$
or, $12x = 408\times 10$
$\therefore x = \dfrac{408\times 10}{12} = 340$
Hence the number of candidates from State Q in 2006 is 340.