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$10$ students of class $X$ took part in a mathematics quiz. If the number of girls is $4$ more than the number of boys, find the number of boys and girls who took part in the quiz by graphical method.

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2, 7

6, 9

3, 12

None of these

answer is D.

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Detailed Solution

Given that 10 students took part in a mathematics quiz.
Let number of boys be

x

, number of girls be

y

.
Given that total number of student is

10

so that

x + y = 10

.
Subtract

y

both side we get,

x = 10 –y

Putting

y = 0, 5, 10

we get,

x = 10 - 0 = 10

x = 10 - 5 = 5

x = 10 - 10 = 0

Therefore, the required points are

(0, 10), (5, 5), (10, 0)

.
Given that, if the number of girls is

4

more than the number of boys,
So that

y = x + 4

Putting

x = - 4, 0, 4

, and we get,

y = - 4 + 4 = 0

y = 0 + 4 = 4

y = 4 + 4 = 8

Therefore, the required points are

(- 4, 0), (0, 4), (4, 8)

.
Plotting the points to form the line,
Question Image

Since the point of intersection in the above graph is

(3, 7)

,thus, the number of boys are

3

and the number of girls are

7

.
Therefore, option (4) is correct.

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