School strength split: In a certain school, the ratio of boys to girls is 7 : 5 and the total number of students is 2400. Determine the exact number of girls by applying the part-of-whole method.

Introduction / Context:
A two-part ratio and a total allow direct computation of each subgroup by converting the ratio into fractional shares of the whole. This is a staple ratio-to-quantity application.

Given Data / Assumptions:

• Boys : Girls = 7 : 5.
• Total students = 2400.

Concept / Approach:
Sum of parts = 7 + 5 = 12. Girls represent 5/12 of the total. Multiply the total by 5/12 to get the number of girls.

Step-by-Step Solution:

Verification / Alternative check:
Boys = (7/12)*2400 = 1400. Sum = 1400 + 1000 = 2400 matches the total; the ratio 1400:1000 reduces to 7:5.

Why Other Options Are Wrong:
500, 700, 800, and 1200 are not equal to 5/12 of 2400 and do not preserve the 7 : 5 split with 2400 total.

Common Pitfalls:
Dividing 2400 by only one of the ratio numbers or using 5/7 rather than 5/12; always divide by the sum of the ratio parts first.

Final Answer:
1000