Q. 255.0( 4 Votes )

A shopkeeper buys

Answer :

We need to find the number of books he bought, so let the number of books he bought be x.

According to the question, the shopkeeper bought 4 more books for the same amount.


It is depicted mathematically as, x + 4


The amount for which these books are bought by the shopkeeper = Rs.80


‘If he had bought 4 more books for the same amount, each book would have cost Rs.1 less’ is depicted as,




80x + 320 – 80x = x2 + 4x


x2 + 4x – 320 = 0


x2 + 20x – 16x – 320 = 0


x(x + 20) – 16(x + 20) = 0


(x – 16)(x + 20) = 0


x – 16 = 0 or x + 20 = 0


x = 16 or x = -20


Since, books cannot be in a negative number so number of books bought is 16.


Or


Let one number be x and the other number be y.


, sum of two numbers be 9 x + y = 9


y = 9 – x


Also, sum of their reciprocals be 1/2.




[, y = 9 – x]


18 = 9x – x2


x2 – 9x + 18 = 0


x2 – 6x – 3x + 18 = 0


x(x – 6) – 3(x – 6) = 0


(x – 3)(x – 6) = 0


x – 3 = 0 or x – 6 = 0


x = 3 or x = 6


When x = 3, y = 9 – 3 y = 6


When x = 6, y = 9 – 6 y = 3


Thus, the numbers are 3 and 6 or the numbers are 6 and 3.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses