Question

A shopkeeper earns a profit of Re.1 by selling one pen and incurs a loss of 40 paisa per pencil while selling pencils of her old stock. In a particular month, she incurs a loss of Rs.5 In this period, she sold 45 pens. How many pencils did she sell in this period?

Answer 1

Hint: First of all, we will find the profit earned by selling 45 pens by multiplying the profit per pen i.e. Re.1 and 45, then we will suppose the number of pencils that the shopkeeper sold as x and then, we will find the loss due to selling pencils. After that, we will form an equation according to the given condition that the shopkeeper incurs a loss of Rs.5 in this period.

Complete step by step solution:
We have been given that, a shopkeeper earns a profit of Rs.1 by selling one pen and incurs a loss of 40 paisa per pencil while selling pencils of her old stock. In a particular month, she incurred a loss of Rs.5 and she sold 45 pens, so we have to find the number of pencils that she sold.
By selling 1 pen profit = Rs.1
So, by selling 45 pen profit \[\Rightarrow Rs\left( 45\times 1 \right)\Rightarrow Rs.45\]
Let us suppose, the number of pencils that was sold to be x.
Since, by selling 1 pencil loss = 40 paisa
So, by selling x pencil loss \[\Rightarrow \left( 40\times x \right)\Rightarrow 40x\text{ paisa}\]
We know that \[1\text{ paisa = Rs}\text{.}\dfrac{1}{100}\]
By selling x pencil loss \[\Rightarrow Rs.\dfrac{40x}{100}\Rightarrow Rs.0.4x\]
Now, according to question,
\[45-\left( 0.4x \right)=-5\]
Here, negative sign before a quantity indicates that, the corresponding quantity is a loss, since, we know that profit and loss are complementary to each other,
\[\begin{align}
  & \Rightarrow 45+5=0.4x \\
 & \Rightarrow 50=0.4x \\
 & \Rightarrow \dfrac{50}{0.4}=x \\
 & \Rightarrow x=125 \\
\end{align}\]
Hence, there are 125 pencils that the shopkeeper sold in this period.

Note: The sign convention is very important in this question, as you can do mistake while forming the equation and you will write the equation as \[45-\left( 0.4x \right)=5\] which is absolutely incorrect as you consider (0.4x) as loss, but you forget that 5 is also a loss. So, we must put negative signs before it.