In a school there are 1400 students. Of these, 25% wear spectacles and 2/7 of those wearing spectacles are boys. How many girls in the school wear spectacles?

Introduction / Context:
This question is about percentages and fractions applied one after another. First, a percentage of the total students are identified as wearing spectacles. Then, among those, a fraction are boys, and the rest are girls. We are asked to find how many girls wear spectacles. This combines percentage calculation with simple ratio reasoning.

Given Data / Assumptions:

• Total number of students in the school = 1400.
• 25% of the students wear spectacles.
• Among those who wear spectacles, 2/7 are boys.
• The remaining spectacle wearers are girls.

Concept / Approach:
First we compute the total number of students who wear spectacles by taking 25% of 1400. Then we apply the fraction 2/7 to that number to find how many of those are boys. Finally the number of girls who wear spectacles equals total spectacle wearers minus spectacle wearing boys. This stepwise approach ensures we use both the percentage and fractional information correctly.

Step-by-Step Solution:
Step 1: Total students = 1400. Step 2: Percentage of students wearing spectacles = 25%. Step 3: Number of students wearing spectacles = 25% of 1400 = (25 / 100) * 1400. Compute 25% of 1400 = 0.25 * 1400 = 350. Step 4: Of these 350 spectacle wearers, 2/7 are boys. Number of boys wearing spectacles = (2 / 7) * 350. (2 / 7) * 350 = 2 * 50 = 100. Step 5: Number of girls wearing spectacles = total spectacle wearers - boys wearing spectacles. Girls wearing spectacles = 350 - 100 = 250. Step 6: Therefore, 250 girls in the school wear spectacles.

Verification / Alternative check:
We can also compute directly the fraction of total students who are girls wearing spectacles. Spectacle wearers are 25% of 1400, that is 350. Of these, 2/7 (or about 28.57%) are boys, so 5/7 (or about 71.43%) must be girls. 5/7 of 350 = 5 * 50 = 250. This agrees with our earlier result, confirming that 250 is correct.

Why Other Options Are Wrong:
100 corresponds to the number of boys wearing spectacles, not girls. 200 and 300 do not satisfy the fraction 2/7 for boys when combined with 1400 total students and 25% spectacle wearers. Only 250 fits consistently with all pieces of information given in the problem.

Common Pitfalls:
A common mistake is to take 2/7 of the total number of students, instead of 2/7 of only those who wear spectacles. Another mistake is to miscalculate 25% of 1400 or to wrongly subtract when computing the girls. Carefully tracking which group each percentage or fraction applies to is essential in such layered percentage problems.

Final Answer:
The number of girls in the school who wear spectacles is 250.