Question

A milkman sold two of his buffaloes for $\mathrm{Rs}.20,000$ each. On one he made a gain of $5\%$ and on the other a loss of $10\%$. Find his overall gain or loss. Find CP of each

Answer 1

Step 1: Solve for the cost price of buffalo that was sold for profit

Given, the selling price (SP) of each buffalo is $\mathrm{Rs}.20,000$

The gain he made on one of the buffaloes is $5\%$

We know that,
$\text{Gain}\%=\frac{\text{SP}-\text{CP}}{\text{CP}}\times 100$

Here, $\text{Gain}\%=5\%$, $\text{SP}=\text{Rs}.20,000$. So we have,
$\begin{array}{cc}& 5=\frac{20,000-\text{CP}}{\text{CP}}\times 100\\ \Rightarrow & 5\text{CP}=20,00,000-100\text{CP}\\ \Rightarrow & 105\text{CP}=20,00,000\\ \Rightarrow & \text{CP}=\text{Rs}.19,047.62\end{array}$

Step 2: Solve for the cost price of buffalo that was sold for loss

We know that,
$\text{Loss}\%=\frac{\text{CP}-\text{SP}}{\text{CP}}\times 100$

Here, $\text{Loss}\%=10\%$, $\text{SP}=\text{Rs}.20,000$. So we have,
$\begin{array}{cc}& 10=\frac{CP-20,000}{\text{CP}}\times 100\\ \Rightarrow & 10\text{CP}=100\text{CP}-20,00,000\\ \Rightarrow & 90\text{CP}=20,00,000\\ \Rightarrow & \text{CP}=\text{Rs}.22,222.22\end{array}$

Step 3: Solve for overall gain or loss

Total purchasing price is $19,047.62+22,222.22=\text{Rs}.41269.84$

Total selling price is $20,000+20,000=\text{Rs}.40,000$

Clearly, selling price is less than cost price so he incurred a loss.

His overall loss percentage is,
$Loss\%=\frac{\text{CP-SP}}{\text{CP}}\times 100$

$\begin{array}{rcl}\text{Loss}\%& =& \frac{41,269.84-40,000}{41,269.84}\times 100\\ & =& \frac{1,269.84}{41,269.84}\times 100\\ & =& 3.08\%\end{array}$

Therefore, the cost prices of the buffaloes were $\text{Rs}.19,047.62$ and $\text{Rs}.22,222.22$ and he incurred a loss of $3.08\%$.