Question

The cost of 2 pens and one pencil is Rs. 35. The cost of 3 pens and 4 pencils is Rs. 65. What is the cost of one pen?
(a) 20
(b) 30
(c) 15
(d) 35

Answer 1

Hint: In this question, we first need to assume the cost of each pen and pencil as some variables. Then from the given conditions in the question we get two linear equations in terms of cost of each pen and pencil of the form \[ax+by+c=0\]. Now, solving these two equations further gives the result.

Complete step by step solution:
Let us assume the cost of each pen as x and the cost of each pencil as y.
Now, given that cost of 2 pens and one pencil is Rs.35
As we already know that general form of a linear equation in two variables is given by
\[ax+by+c=0\]
Let us now substitute the respective values accordingly,
\[\Rightarrow 2x+y=35........\left( 1 \right)\]
Now, given that the cost 3 pens and 4 pencils is Rs.65
Now, from the general form of linear equation in two variables we have
\[ax+by+c=0\]
Now, on substituting the respective values and forming the linear equation we get,
\[\Rightarrow 3x+4y=65........\left( 2 \right)\]
Now, from the given conditions we have the equations (1) and (2) as
\[\begin{align}
  & \Rightarrow 2x+y=35 \\
 & \Rightarrow 3x+4y=65 \\
\end{align}\]
Let us now multiply the equation (1) with 4 and simplify further
\[\begin{align}
  & \Rightarrow 8x+4y=140 \\
 & \Rightarrow 3x+4y=65 \\
\end{align}\]
Let us now subtract these two equations then we get,
\[\Rightarrow 8x-3x=140-65\]
Now, on further simplification we get,
\[\Rightarrow 5x=75\]
Let us now divide with 5 on both the sides
\[\Rightarrow x=\dfrac{75}{5}\]
Now, on further simplification we get,
\[\therefore x=15\]
Hence, the correct option is (c).

Note:
Instead of assuming the cost of pencil and pen as variables from the first condition given we get the cost of each pencil in terms of cost of pen. Then on substituting in the second condition we can directly get the cost of each pen. Both the methods give the same result.
It is important to note that while simplifying the equations by arithmetic operation and rearranging we should not neglect any of the terms or write the incorrect value because it changes the final result.