Question

A farmer bought a buffalo for $₹44000$ and a cow for $₹18000$. He sold the buffalo at a loss of $5\%$ but made a profit of $10\%$ on the cow. The net result of the transaction is

• A. loss of $₹200$
• B. profit of $₹400$
• C. loss of $₹400$
• D. profit of $₹200$

Answer 1

The correct option is C

loss of $₹400$

Step 1: Finding the selling price of the cow

We have,

Cost price of cow$=₹18000$

Profit percent on cow$=10\%$

We know that,

$\mathrm{Profit}\%=\frac{\mathrm{Profit}}{\mathrm{Cost}\mathrm{price}}\times 100$

$$\begin{gathered} \Rightarrow 10=\frac{\mathrm{Profit}}{18000}\times 100 \\ \Rightarrow \frac{10\times 18000}{100}=\mathrm{Profit} \\ \Rightarrow \mathrm{Profit}=10\times 180 \\ \Rightarrow \mathrm{Profit}=₹1800 \end{gathered}$$

Then,

$$\begin{gathered} \mathrm{Profit}=\mathrm{Selling}\mathrm{price}\left(\mathrm{SP}\right)–\mathrm{Cost}\mathrm{price}\left(\mathrm{CP}\right) \\ \Rightarrow 1800=\mathrm{SP}–18000 \\ \Rightarrow \mathrm{SP}=1800+18000 \\ \Rightarrow \mathrm{SP}\mathrm{of}\mathrm{cow}=₹19800 \end{gathered}$$

Step 2: Finding the selling price of the buffalo

We have,

Cost price of buffalo$=₹44000$

He sold the buffalo at a loss of $5\%$

We know that,

$$\begin{gathered} \mathrm{Loss}\%=\frac{\mathrm{Loss}}{\mathrm{Cost}\mathrm{Price}}\times 100 \\ \Rightarrow 5=\frac{\mathrm{Loss}}{44000}\times 100 \\ \Rightarrow \frac{5\times 44000}{100}=\mathrm{Loss} \\ \Rightarrow \mathrm{Loss}=5\times 440 \\ \Rightarrow \mathrm{Loss}=₹2200 \end{gathered}$$

Then,

$$\begin{gathered} \mathrm{Loss}=\mathrm{CP}–\mathrm{SP} \\ \Rightarrow 2200=44000–\mathrm{SP} \\ \Rightarrow \mathrm{SP}=44000–2200 \\ \Rightarrow \mathrm{SP}\mathrm{of}\mathrm{buffalo}=₹41,800 \end{gathered}$$

Step 3: Calculating net profit/loss

Now,

Total cost price of both buffalo and cow$=44000+18000=₹62000$

Total selling price of both buffalo and cow$=41800+19800=₹61,600$

The selling price of both buffalo and cow is less when compared to cost price,

So,

$$\begin{gathered} \mathrm{Loss}=\mathrm{CP}–\mathrm{SP} \\ \Rightarrow \mathrm{Loss}=62000-61600 \\ \Rightarrow \mathrm{Loss}=₹400 \end{gathered}$$

Hence, there is net loss of $₹400$ in the whole transaction.