Question 705009

SCQMEDIUM

In a class of 70 students, 20%20\% of girls have spectacles and 40%40\% of boys have spectacles. If the total number of students having spectacle is 23, the number of boys in the class is

(A)

45

(B)

14

(C)

18

(D)

25

Detailed Solution

Let bb be the number of boys and gg be the number of girls.

Given b+g=70b + g = 70, so g=70−bg = 70 - b.

The number of students with spectacles is 0.4b+0.2g=230.4b + 0.2g = 23.

Substituting gg: 0.4b+0.2(70−b)=230.4b + 0.2(70 - b) = 23 ⇒0.4b+14−0.2b=23\Rightarrow 0.4b + 14 - 0.2b = 23 ⇒0.2b=9\Rightarrow 0.2b = 9 ⇒b=90.2=45\Rightarrow b = \frac{9}{0.2} = 45.

Therefore, the number of boys is 45.

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