RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 10. Quadratic Equations

Subject: Maths - Class 10th

Q. No. 30 of Exercise 10E

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30

300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.

Let the total number of students be x

According to the question



taking LCM



cross multiplying



Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = 10 c = – 3000


= 1. – 3000 = – 3000


And either of their sum or difference = b


= 10


Thus the two terms are 60 and – 50


Difference = 60 – 50 = 10


Product = 60. – 50 = – 3000


x2 + 60x – 50x – 3000 = 0


x(x + 60) – 50(x + 60) = 0


(x + 60) (x – 50) = 0


(x – 50) = 0 or (x + 60) = 0


x = 50 or x = – 60


x cannot be negative thus total number of students = 50


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