A sum of Rs 312 is divided among 100 children consisting of boys and girls so that each boy receives Rs 3.60 and each girl receives Rs 2.40. How many girls are there in the group?

Introduction / Context:
This problem combines simple linear equations with an everyday context of distributing money among boys and girls. It tests the ability to translate a word problem into algebraic equations and to work with two variables under given constraints.

Given Data / Assumptions:

• Total number of children (boys plus girls) = 100
• Total amount distributed = Rs 312
• Each boy gets Rs 3.60
• Each girl gets Rs 2.40
• We must determine the number of girls.

Concept / Approach:
Let the number of boys and girls be variables. Use the information about total number of children to form one equation, and the information about total money distributed to form another equation. Solving these two simultaneous equations will give us the required numbers. This is a classic two variable linear equation setup frequently asked in aptitude exams.

Step-by-Step Solution:
Step 1: Let the number of boys be b and the number of girls be g. Step 2: From the total headcount, we have b + g = 100. Step 3: Each boy gets Rs 3.60 and each girl gets Rs 2.40, so total amount is 3.60b + 2.40g = 312. Step 4: Divide the second equation by 1.2 to simplify: 3b + 2g = 260. Step 5: Now we have the system: b + g = 100 and 3b + 2g = 260. Step 6: Multiply the first equation by 2: 2b + 2g = 200. Step 7: Subtract this from 3b + 2g = 260 to get b = 60. Step 8: Substitute b = 60 into b + g = 100 to get g = 40.

Verification / Alternative check:
With 60 boys and 40 girls, total amount distributed is 60 * 3.60 + 40 * 2.40. That equals 216 + 96 = 312, which matches the given total. Also, the headcount 60 + 40 is 100. Therefore, the calculated numbers satisfy both conditions and confirm that the answer is correct.

Why Other Options Are Wrong:
If we assume 35, 45, 50 or 30 girls, the resulting number of boys will not satisfy both the total amount and total children conditions simultaneously. Either the total money will not sum to Rs 312 or the headcount will not be exactly 100. Hence those options are inconsistent with at least one of the given equations.

Common Pitfalls:
A common mistake is to forget to convert the rupee values properly when removing decimals, or to mix up the coefficients when forming the total amount equation. Some learners try to solve by guessing combinations instead of setting up equations; this can be slow and error prone. It is always safer to write the equations clearly and solve them systematically.

Final Answer:
The number of girls in the group is 40.