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.
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?
191
195
187
183
179
Solution
Let the percentage of candidates who qualify from State Q in 2010 be $x\%$.
Then,
Average $=\dfrac{\dfrac{280\times 60}{100}-\dfrac{550\times 50}{100}+400\times x\%}{3}=210$
or, $168 + 275 + 4x = 630$
or, $4x = 630-443=187$
$x=\dfrac{187}{4}=46.75\%$
$\therefore$ The number of qualified candidates from State Q in 2010 $= 400\times \dfrac{46.75}{100} = 187$