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%
--
In 2007, the respective ratio of number of appeared candidates to the qualified candidates was 5 : 4. Number of female qualified candidates constitutes what per cent of number of appeared candidates in the same year?
(A) (1) 20
(B) (2) 25
(C) (3) 30
(D) (4) 15
(E) (5) 40
1. **Problem Statement:**
Find the percentage of female qualified candidates out of the total appeared candidates in 2007 given:
- Ratio of appeared to qualified candidates in 2007 is $5:4$.
- Ratio of qualified male to female candidates in 2007 is $5:3$.
2. **Step 1: Define variables**
Let the number of appeared candidates in 2007 be $A$.
Then, number of qualified candidates in 2007 is $Q$.
Given ratio of appeared to qualified candidates:
$$\frac{A}{Q} = \frac{5}{4} \implies Q = \frac{4}{5}A$$
3. **Step 2: Use ratio of qualified male to female candidates**
Let qualified male candidates be $M$ and qualified female candidates be $F$.
Given:
$$\frac{M}{F} = \frac{5}{3}$$
So,
$$M = \frac{5}{3}F$$
Since total qualified candidates $Q = M + F$,
$$Q = \frac{5}{3}F + F = \frac{8}{3}F$$
4. **Step 3: Express $F$ in terms of $Q$**
$$F = \frac{3}{8}Q$$
5. **Step 4: Substitute $Q$ from Step 2**
$$F = \frac{3}{8} \times \frac{4}{5}A = \frac{3 \times 4}{8 \times 5} A = \frac{12}{40} A = \frac{3}{10} A$$
6. **Step 5: Calculate percentage of female qualified candidates out of appeared candidates**
$$\text{Percentage} = \frac{F}{A} \times 100 = \frac{3}{10} \times 100 = 30\%$$
**Final Answer:** Female qualified candidates constitute $30\%$ of appeared candidates in 2007.
**Answer choice:** (C) 30