A man buy two watches at Rs.4000. He sold one watch at 20% profit and second at 10% loss. In this transaction the overall profit or loss will be 5%.Find the cost price of first watch.

The correct option is Rs.2000.

Step-by-step Explanation:

Given Data:

Total cost price of two watches = Rs. 4000

Profit on the first watch = 20%

Loss on the second watch = 10%

Overall profit on the whole transaction = 5%

Step 1: Define the variables

Let the cost price of the first watch be ${\mathrm{CP}}_1$ = $x$.

Then, the cost price of the second watch ${\mathrm{CP}}_2$ = $4000-x$.

Step 2: Set up the equation using profit and loss

Profit from the first watch = $20\%\text{of}x=\frac{20}{100}x$

Loss from the second watch = $10\%\text{of}(4000-x)=\frac{10}{100}(4000-x)$

Overall profit = $5\%\text{of}4000=\frac{5}{100}\times 4000=200$

Total gain/loss equation:

$\frac{20}{100}x-\frac{10}{100}(4000-x)=200$

Step 3: Solve for $x$

Multiply the entire equation by 100 to eliminate denominators:

$20x-10(4000-x)=20000$

$20x-40000+10x=20000$

$30x=20000+40000$

$30x=60000$

$x=\frac{60000}{30}=2000$

Therefore, the cost price of the first watch is Rs.2000.