Q9 of 58 Page 108

In a class of 60 students, each boy contributed rupees equal to the number of girls and each girl contributed rupees equal to the number of boys. If the total money then collected was D 1600. How many boys are there in the class?

Let the number of girls be x and number of boys be y

Given that the total number of students = 60


⇒ x + y = 60 ⇒ y = 60 –x


Total money collected = 1600


According to the given condition


1600 = xy + yx


⇒ 1600 = 2 xy


⇒ xy = 800


⇒ x( 60 –x) = 800


⇒ x2 - 60x + 800 = 0


⇒ x2 – 20x – 40x + 800 = 0


⇒ x ( x – 20) – 40 (x – 20) = 0


⇒ (x - 40) (x - 20) = 0


⇒ x = 40 or 20


Hence if the number of girls is 40, then the number of boys is 20


And if the number of girls is 20, then the number of boys is 40.


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