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: Here we go through by making the two equations as there are two variables by letting the price of one pen be x and the price of one pencil be y. By solving the equations we get our result.

Complete step-by-step answer:
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 pencil are Rs.30 i.e.
5x+10y=30
By taking 5 as common and dividing both side we get,
x+2y=6
Let it be as equation (1).
Also given that a pen cost 3 more than a pencil
i.e. x=3+y
Let it be as an equation (2).
Now subtract equation (2) from equation (1) one we get,
$ \Rightarrow $3y=3
$\therefore $y=1
Now put the value of y in equation (2) we get,
$ \Rightarrow $x=3+1=4
Therefore the cost of a pen is Rs. 1 and the cost of a pencil is Rs. 4.

Note: Whenever we face such 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.