Question

A horse and a cow were sold for Rs. 49,500 each. The horse was sold at a loss $10%$ and the cow at a gain of $10%$. The entire transaction resulted in?

Answer 1

Hint: First, we will find the cost price for each using the formulas. The formula of C.P for $10%$ loss is $S.P=C.P-C.P\times \dfrac{10}{100}$ and the formula of C.P for $10%$ gain is $S.P=C.P+C.P\times \dfrac{10}{100}$.
After finding the C.P for each. We will find how much gain or loss occurred by using the formula $\dfrac{\text{total S}\text{.P - total C}\text{.P}}{\text{total C}\text{.P}}\times 100$.

Complete step-by-step answer:
The horse and cow were sold for Rs. 49,500 each. So, the total selling price will be,
$\begin{align}
  & =49,500+49,500 \\
 & =Rs.99000 \\
\end{align}$
The horses were sold at a loss $10%$. Now, we will find the actual cost price of horse using the formula,
$S.P=C.P-C.P\times \dfrac{10}{100}$
S.P of horse = 49,500
Substituting S.P in LHS and taking LCM of terms on RHS, we get
$\begin{align}
  & 49,500=\dfrac{100C.P-10C.P}{100} \\
 & \Rightarrow 49,500=C.P\times \dfrac{90}{100} \\
 & \Rightarrow C.P=\dfrac{49,500\times 100}{90} \\
 & \Rightarrow C.P=55,000 \\
\end{align}$
The actual cost price of horse is Rs. 55,000………(1)
Now, the cows were sold at a gain of $10%$.
So, we will find the actual cost of price of cow by using the formula,
$S.P=C.P+C.P\times \dfrac{10}{100}$
S.P of cow = 49,500
Substituting S.P in LHS and taking LCM of terms on RHS, we get
$\begin{align}
  & 49,500=\dfrac{100C.P+10C.P}{100} \\
 & \Rightarrow 49,500=C.P\times \dfrac{110}{100} \\
 & \Rightarrow C.P=\dfrac{49,500\times 110}{100} \\
 & \Rightarrow C.P=45,000..........\left( 2 \right) \\
\end{align}$
The C.P cost price) of cow = Rs. 45,000.
Now, to find the entire transaction result, we will use the formula,
$\dfrac{\text{S}\text{.P - C}\text{.P}}{\text{C}\text{.P}}\times 100$
Now, the total cost price is from equation (1) & (2).
$\begin{align}
  & =55,000+45,000 \\
 & =Rs.100,000 \\
\end{align}$
The total selling price is,
$\begin{align}
  & =49,500+49,500 \\
 & =Rs.99000 \\
\end{align}$
Clearly we can see that the cost price is higher than the selling price. So, there will be loss. The loss percentage is,
   $=\dfrac{99,000-100,000}{100,000}\times 100 \\$
  $=\dfrac{-1000}{100,000}\times 100 \\$
  $=-1% \\ $
The negative sign represents loss.
The entire transaction resulted in loss of $1%$.

Note: The students can make mistakes in applying the formula. For loss they can use the formula that is $S.P=C.P+C.P\times \dfrac{10}{100}$ and for gain, they can use the formula that is $S.P=C.P-C.P\times \dfrac{10}{100}$. But as we know that for loss, the selling price is less than the cost price. So, the formula will be $S.P=C.P-C.P\times \dfrac{10}{100}$ and for gain, the selling price is higher than the cost price. So, the formula will be $S.P=C.P+C.P\times \dfrac{10}{100}$.