There are 200 students in a school, of which seven-tenths are boys. How many girls are there in the school?

Introduction / Context:
This is a basic ratio and fraction problem. We are told what fraction of the total students are boys and are asked to find how many students are girls. It tests the ability to convert fractional information about a group into actual numbers.

Given Data / Assumptions:

• Total number of students in the school = 200.
• Fraction of students who are boys = 7/10.
• We assume all students are either boys or girls; there is no other category.

Concept / Approach:
If 7/10 of the students are boys, then the remaining 3/10 must be girls because the total fraction must add up to 1 (or 10/10). The number of boys is (7/10) of 200, and the number of girls is total students minus the number of boys or directly (3/10) of 200. Either method gives the same result.

Step-by-Step Solution:
Step 1: Compute the number of boys. Boys = (7 / 10) * 200 = 7 * 20 = 140. Step 2: Compute the number of girls from the total. Girls = total students - boys = 200 - 140 = 60. Alternative: Girls = (3 / 10) * 200 = 3 * 20 = 60.

Verification / Alternative check:
We can verify by checking that the sum of boys and girls matches the total. Boys = 140, girls = 60, so total = 140 + 60 = 200, which matches the given total number of students. Also, boys fraction = 140 / 200 = 7 / 10, and girls fraction = 60 / 200 = 3 / 10, which are complementary fractions adding up to 1, confirming correctness.

Why Other Options Are Wrong:
Option a (80) would give boys = 120 and girls = 80, so boys fraction would be 120 / 200 = 3/5, not 7/10. Option c (40) would give boys = 160 and boys fraction 160 / 200 = 4/5. Option d (120) would give boys = 80 and boys fraction 80 / 200 = 2/5. None of these matches the specified 7/10 fraction for boys. Only 60 yields the correct distribution.

Common Pitfalls:
One common mistake is to multiply the total by 3/10 instead of 7/10 when finding boys, or to misinterpret 7/10 as 7%. Another is forgetting that the remaining fraction automatically belongs to the other group. Always check that fractions for all groups add up to 1 and that the calculated numbers sum to the total.

Final Answer:
The number of girls in the school is 60.