Rs. 41 is distributed among 50 students (boys and girls). Each boy receives 90 paise while each girl receives 65 paise. Find the exact number of boys.

Introduction / Context:
Allocation problems with different per-person amounts are solved using simultaneous linear equations. Here, the total number of students is known, and the total payout is fixed, with boys and girls receiving different amounts (in paise).

Given Data / Assumptions:

• Total students = 50.
• Total money = Rs. 41 = 4100 paise.
• Boy gets 90 paise; girl gets 65 paise.

Concept / Approach:
Let b = number of boys, g = number of girls. Then b + g = 50 and 90b + 65g = 4100 (all in paise). Solve these equations to get b and g as integers satisfying both constraints.

Step-by-Step Solution:
b + g = 50 … (1) 90b + 65g = 4100 … (2) From (1), g = 50 − b. Substitute in (2): 90b + 65(50 − b) = 4100 ⇒ 90b + 3250 − 65b = 4100. 25b = 850 ⇒ b = 34; then g = 16.

Verification / Alternative check:
34 boys * 90 = 3060 paise; 16 girls * 65 = 1040 paise; total = 4100 paise = Rs. 41, so the values fit perfectly.

Why Other Options Are Wrong:
16, 14, 36 do not satisfy both equations simultaneously; substituting any of them breaks the total amount constraint or headcount.

Common Pitfalls:
Forgetting to convert rupees to paise consistently or mixing up which variable stands for boys versus girls. Keep units consistent throughout.

Final Answer:
34