Question

The total cost of 5 pens and 10 pencils is Rs.30. If a pen costs Rs.3 more than a pencil, find the price of each item.

Answer 1

Hint: First assume the cost of the pen and the pencil. After that make one equation from the total cost and the second equation from the relation between the cost of pen and pencil. Then, use the substitution method to solve the equation and get the cost of one pen and one pencil.

Complete step-by-step solution:
Let the price of one pen be Rs. $x$ and the price of one pencil will be Rs. $y$.
Given that the total cost of 5 pens and 10 pencils is Rs. 30. So, the equation will be,
$ \Rightarrow 5x + 10y = 30$
By taking 5 as common and dividing both sides we get,
$ \Rightarrow x + 2y = 6$.............….. (1)
Also given that a pen costs 3 more than a pencil. So, the equation will be,
$ \Rightarrow x = y + 3$................….. (2)
Substitute the value of $x$ from equation (2) in equation (1),
$ \Rightarrow y + 3 + 2y = 6$
On simplifying the terms, we get
$ \Rightarrow 3y = 3$
Dividing both sides by 3, we get
$ \Rightarrow y = 1$
Now put the value of y in equation (2) we get,
$ \Rightarrow x = 1 + 3$
On adding the terms, we get
$ \Rightarrow x = 4$

Hence, the cost of a pen is Rs. 1 and the cost of a pencil is Rs. 4.

Note: Whenever we face such a type of question the key concept for solving the question is to make the equation by the given data in the question as we know if there are two variables there must be two equations for finding these two variables. We can solve these types of questions by elimination method as well.
An equation is said to be a linear equation in two variables if it is written in the form of \[ax + by + c = 0\], where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.