Directions : Study the given table carefully and answer the questions that follow : Number of candidates appeared and qualified for a test (in hundreds) in 6 different years from 5 different zones. (Bank P.O., 2011) | Year | P App. | P Qual. | Q App. | Q Qual. | R App. | R Qual. | S App. | S Qual. | T App. | T Qual. | |---|---|---|---|---|---|---|---|---|---|---| | 2005 | 3.2 | 2.5 | 3.5 | 1.4 | 3.8 | 2.2 | 4.2 | 2.4 | 6.2 | 2.6 | | 2006 | 4.6 | 3.4 | 6.9 | 4.2 | 6.9 | 4.4 | 7.4 | 3.3 | 6.2 | 4.8 | | 2007 | 6.5 | 4.9 | 7.7 | 4.5 | 5.9 | 4.8 | 8.3 | 5.6 | 6.4 | 4.2 | | 2008 | 7.4 | 5.7 | 5.4 | 3.4 | 7.2 | 3.2 | 9.3 | 6.4 | 7.8 | 6.2 | | 2009 | 8.8 | 4.8 | 6.6 | 5.2 | 8.6 | 6.8 | 11.4 | 5.2 | 9.9 | 6.9 | | 2010 | 9.2 | 5.6 | 10.6 | 6.4 | 10.3 | 7.4 | 14.2 | 11.4 | 11.8 | 9.4 | Note: Here App. means Appeared and Qual. means Qualified. What was the ratio of the number of candidates appeared from zone P in the year 2005 to the number of candidates qualified from zone S in the year 2007 ?

### Concept & Ratios A ratio compares two quantities by division. To find the ratio of $A$ to $B$, simply write it as a fraction $A / B$ and simplify it to its lowest terms. $$ \text{Ratio} = \frac{\text{Value A}}{\text{Value B}} $$ ### Step-by-Step Solution 1. **Identify Value A:** Number of candidates appeared from zone P in 2005. From the table, P (App.) in 2005 is $3.2$. 2. **Identify Value B:** Number of candidates qualified from zone S in 2007. From the table, S (Qual.) in 2007 is $5.6$. 3. **Form Ratio:** $$ \text{Ratio} = \frac{3.2}{5.6} $$ 4. **Simplify:** Multiply both numerator and denominator by 10 to remove decimals, resulting in $\frac{32}{56}$. Both numbers are divisible by 8. $$ \frac{32 \div 8}{56 \div 8} = \frac{4}{7} $$ ### Exam Strategy & Shortcut When you see $3.2$ and $5.6$, immediately recognize them as multiples of the $8$ times table ($8 \times 4 = 32$ and $8 \times 7 = 56$). This lets you bypass writing out the fraction and directly select $4 : 7$. ### Common Pitfall Pulling the wrong data points (e.g., taking P qualified instead of appeared, or S appeared instead of qualified) is the most common error in matrix table lookups. Always double-check column headers. ### Final Answer Therefore, the correct answer is **4 : 7**.