Question

Student of class 10 collected rupees 9000.They wanted to divide it equally among a certain number of students residing in slum areas.When they started distributing the amount 20 more students from nearby slum also joined.now each student got 160 less.
Find the original number of students living in slum

Answer 1

Answer:

Let the original number of students be x, then

9000 divided equally between x persons, each one get ------> 9000/x

9000 divided equally between (x + 20) persons, each one get------> 9000/(x + 20)

According to the condition,

9000/(x + 20) = 9000/x - 160

=> 9000x = (x+20)(9000 - 160x)

=> 9000x = 9000x - 160x^2 + 180000 - 3200x

=> 160x^2 + 3200x - 180000 = 0

=> x^2 + 20x - 1125 = 0

=> x^2 + 45x - 25x - 1125 = 0

=> x(x + 45) - 25(x + 45) = 0

=> (x + 45)(x - 25) = 0

   Either (x + 45) = 0 or ( x - 25) = 0

   (x + 45) = 0 => x = - 45 (not possible)

   Therefore, (x - 25) = 0

=> x = 25. ans

ANSWER

x = 25