Ten class X students took part in a math quiz. If the number of girls is 4 more than the number of boys, how many boys and girls answered the quiz?

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no. of girls=7, no. of boys=3

no. of girls=8, no. of boys=3

no. of girls=4, no. of boys=7

no. of girls=8, no. of boys=4

answer is A.

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Detailed Solution

Given that number of students participated in a Mathematics quiz = 10.
Let the number of girls and boys be x and y respectively.
Total number of students = number of girls + number of boys.
The total number of students in algebraic form is,

x + y = 10 ⇒ x = 10 − y ......... (1)

Given number of girls is 4 more than the number of boys. So,

x = 4 + y

…. (ii)
Find the solutions of x and y by applying the values.
Apply the values to the equations, (1) and (2).

y	6	5	4
x=10-y	4	5	6

y	0	1	-1
x=4+y	4	5	3

Plotting the obtained values in the form of (x, y) on the graph for both equations.
Join the points of the respective equations.
Question Image

Now check whether the lines intersect or not.
From the graph, we can observe (7,3) is the intersecting points of lines x+ y=10 and x- y = 4.
Thus, the required solution (x, y) is (7, 3).
The number of girls who took part in the quiz = 7.
The number of boys who took part in the quiz = 3.
Therefore, the correct option is 1.

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