Question

If Rs $ 50 $ is to be distributed among $ 150 $ students giving $ 50 $ paisa to each boy and $ 25 $ paisa to each girl, then the number of boys is
A. $ 25 $
B. $ 40 $
C. $ 36 $
D. $ 50 $

Answer 1

Hint: This is a problem of linear equations in two variables. The number of boys and the number of girls are unknown. Two equations should be made and solved for a number of boys and girls.

Complete step-by-step answer:
Given information
Total amount of money, $ P = 50{\text{ Rs}} $
Total number of students (including boys and girls both), $ N = 150 $
Amount given to each boy boys, $ p = 50{\text{ paise}} $
Amount given to each girl, $ q = 25{\text{ paise}} $
We are required to determine the number of boys.
It should be understood that there are two variables in the question number of boys and girls.
Let the number of boys and girls be $ x $ and $ y $ respectively.
Then according to question,
The number of students
 $
\Rightarrow x + y = N \\
\Rightarrow x + y = 150 \cdots \left( 1 \right) \;
  $
Also
The total number of money which is to be distributed between boys and girls.
 $ x \times \dfrac{{50}}{{100}} + y \times \dfrac{{25}}{{100}} = 50 \cdots \left( 2 \right) $ ( Rupee is equal to Paisa)
Multiplying equation (2) by $ 100 $ , we get
 $ 50x + 25y = 5000 \cdots \left( 3 \right) $
Dividing equation (3) by $ 25 $ , we get
 $ 2x + y = 200 \cdots \left( 4 \right) $
Subtracting equation (1) from equation (4), we get
 $
\Rightarrow \left( {2x - x} \right) + \left( {y - y} \right) = 200 - 150 \\
\Rightarrow x = 50 \;
  $
Hence, the total number of boys among the total number of students are $ 50 $
So, the correct answer is “Option D”.

Note: The important thing is to realize that all units should be uniform. The money is given rupees and paise, and then it should be converted into one unit either in rupees or paise. But for simplicity it should be converted to rupees.
It should be kept in mind that this problem involves linear equations in two variables.