Question: Study the table and answer the given questions.
Data related to candidates appeared and qualified from State $x$ in a competitive exam during 5 years
Year No. of appeared
candidates \% of appeared
candidates
who qualified Respective ratio of number of
qualified male and number of
qualified female candidates
2006 700 -- 3:2
2007 -- -- 5:3
2008 480 60\% --
2009 -- 42\% 9:5
2010 900 64\% --
The number of appeared candidates increased by 40\% from 2006 to 2011. If 25\% of the appeared candidates qualified in 2011, what was the number of qualified candidates in 2011?
(A) (1) 240
(B) (2) 225
(C) (3) 255
(D) (4) 245
(E) (5) 230
1. **Problem Statement:**
We are given data about the number of candidates who appeared and qualified in a competitive exam from State $x$ over 5 years (2006 to 2010). We know the number of appeared candidates in 2006 was $700$. The number of appeared candidates increased by $40\%$ from 2006 to 2011. We need to find the number of qualified candidates in 2011 if $25\%$ of the appeared candidates qualified that year.
2. **Step 1: Calculate the number of appeared candidates in 2011.**
The number of appeared candidates in 2006 was $700$.
The increase from 2006 to 2011 is $40\%$, so the number of appeared candidates in 2011 is:
$$700 + 0.40 \times 700 = 700 \times (1 + 0.40) = 700 \times 1.40 = 980$$
3. **Step 2: Calculate the number of qualified candidates in 2011.**
Given that $25\%$ of the appeared candidates qualified in 2011, the number of qualified candidates is:
$$25\% \text{ of } 980 = 0.25 \times 980 = 245$$
4. **Final Answer:**
The number of qualified candidates in 2011 is $245$.
This corresponds to option (D) (4) 245.