The total number of students in a school is 2140. If the number of girls in the school is 1200, then what is the ratio of the total number of boys to the total number of girls in the school? (Bank Recruitment, 2009)

### Concept & Ratio To find the ratio of two quantities, we first need their exact values and then divide them, simplifying to the lowest terms. $$ \text{Ratio} = \frac{\text{Value 1}}{\text{Value 2}} $$ ### Step-by-Step Solution * Given total number of students = $2140$. * Given number of girls = $1200$. * Calculate the number of boys by subtracting girls from the total: $2140 - 1200 = 940$. * Set up the ratio of boys to girls: $940 : 1200$. * Simplify the ratio by cancelling the common zero (dividing by 10): $94 : 120$. * Further simplify by dividing both numbers by their greatest common divisor, which is 2: $$ \frac{94}{2} : \frac{120}{2} = 47 : 60 $$ ### Exam Strategy & Shortcut Calculate the number of boys ($940$). Notice that $940$ ends in a $0$, and removing it gives $94$. Half of $94$ is $47$, which is a prime number. Look directly at the given options: only option (c) has $47$ as the first term. You can instantly select it without calculating the denominator's simplified form to save time. ### Common Pitfall Finding the ratio of girls to boys ($60 : 47$) or girls to total students instead of the specifically requested boys to girls. Always double-check the order required by the question! ### Final Answer Therefore, the correct answer is **$47 : 60$**.