Directions: A survey of magazine reading habits of the people living in five cities P, Q, R, S and T is summarised in a table given below. The Column I in the table gives percentage of magazine-readers in each city who read only one magazine a week. The Column II gives the total number of magazine-readers who read two or more magazines a week. Read the table and then answer these questions: | City | I | II | | :--- | :---: | :---: | | P | 75 | 6000 | | Q | 80 | 3500 | | R | 60 | 3000 | | S | 55 | 2700 | | T | 25 | 4200 | Which city has the highest number of magazine-readers who read only one magazine a week?

### Concept & Logic To find the number of readers who read only one magazine a week, we first need the total number of readers (calculated using Column II and the complement of Column I). Then, we take the percentage given in Column I of that total. $$ \text{Readers (Only One)} = \text{Total Readers} - \text{Column II Value} $$ Alternatively: $$ \text{Readers (Only One)} = \left( \frac{\text{Col I}\%}{100\% - \text{Col I}\%} \right) \times \text{Col II Value} $$ ### Step-by-Step Solution Let's calculate the "only one" readers for the relevant options using the derived formula: * **For City P:** Ratio of (Only One) to (Two or more) is $75\% : 25\%$, which is $3:1$. Number of "Only One" = $3 \times 6000 = 18000$. * **For City Q:** Ratio is $80\% : 20\%$, which is $4:1$. Number of "Only One" = $4 \times 3500 = 14000$. * **For City R:** Ratio is $60\% : 40\%$, which is $1.5:1$ (or $3:2$). Number of "Only One" = $1.5 \times 3000 = 4500$. * **For City S:** Ratio is $55\% : 45\%$, which is $11:9$. Number of "Only One" = $\frac{11}{9} \times 2700 = 11 \times 300 = 3300$. * **For City T:** (For completeness) Ratio is $25\% : 75\%$, which is $1:3$. Number of "Only One" = $\frac{1}{3} \times 4200 = 1400$. Comparing the numbers ($18000, 14000, 4500, 3300$), the highest is $18000$, which is City P. ### Exam Strategy & Shortcut **Multiplier Method:** Instead of calculating totals, look at the ratio of Col I to $(100 - \text{Col I})$. City P has a multiplier of $\frac{75}{25} = 3$. So $3 \times 6000 = 18000$. City Q has a multiplier of $\frac{80}{20} = 4$. So $4 \times 3500 = 14000$. Since P starts with a massive base number in Col II ($6000$) and a high multiplier ($3$), it will easily outpace the others. You can visually confirm P is the highest without calculating R, S, or T. ### Common Pitfall Students might mistakenly just look at Column I and assume that the highest percentage ($80\%$ for Q) equates to the highest absolute number. You must apply the percentage to the underlying total population to find absolute values. ### Final Answer **Therefore, the correct answer is P.**