Question

Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, the number of pencils would become 4 times the number of pens. Find the original number of pens and pencils.

Answer 1

Hint- Here, we will proceed by assuming the original number of pens and pencils as two different variables i.e., x and y. Then, we will form two linear equations in two variables and will solve them algebraically.

Complete Step-by-Step solution:
Let us suppose that the original number of pens and pencils be x and y respectively
i.e., Original number of pens = x
Original number of pencils = y
Given originally, Total number of pens and pencils = 40
$ \Rightarrow $Original number of pens + Original number of pencils = 40
$
   \Rightarrow x + y = 40 \\
   \Rightarrow y = 40 - x{\text{ }} \to (1) \\
 $
It is also given that if she has (y+5) pencils as the number of pencils and (x-5) pens as the number of pens then, the number of pencils would become 4 times the number of pens
i.e., If Number of pencils = (y+5) pencils and Number of pens = (x-5) pens then, we can write
Number of pencils in this case = 4(Number of pens in this case)
$ \Rightarrow $(y+5) = 4(x-5)
$ \Rightarrow $y + 5 = 4x – 20
By substituting the value of y from equation (1) in the above equation, we get
$ \Rightarrow $(40 – x) + 5 = 4x – 20
$ \Rightarrow $45 – x = 4x – 20
$ \Rightarrow $4x + x = 45 + 20
$ \Rightarrow $5x = 65
$ \Rightarrow $x = 13
Put x = 13 in equation (1), we get
$ \Rightarrow $y = 40 – 13 = 27
Therefore, the original number of pens and pencils that Reena has are 13 pens and 27 pencils respectively.

Note- In this particular problem, in order to find the values of the two variables i.e., x and y we have used a substitution method. Instead of a substitution method, we can also solve with the help of elimination method in which we will make the coefficients of any one variable the same by multiplying the two equations with some number and then will subtract these two obtained equations.