Mathematics
In a school, a class has 40 students out of which x are girls. If the product of the number of girls and number of boys in the class is 375; the number of boys in the class is :
15
25
15 or 25
15 and 25
Quadratic Equations
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Answer
Total students = 40
No. of girls = x
No. of boys = 40 - x
Given,
Product of number of girls and number of boys = 375
⇒ x(40 - x) = 375
⇒ 40x - x2 = 375
⇒ x2 - 40x + 375 = 0
⇒ x2 - 25x - 15x + 375 = 0
⇒ x(x - 25) - 15(x - 25) = 0
⇒ (x - 15)(x - 25) = 0
⇒ (x - 15) = 0 or (x - 25) = 0
⇒ x = 15 or x = 25.
If x = 15,
No. of boys = 40 - x = 40 - 15 = 25.
If x = 25,
No. of boys = 40 - x = 40 - 25 = 15.
Hence, Option 3 is the correct option.
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