A merchant bought two watches for ₹9,000 each. He sold one watch at a loss of 10%.
At what price (in ₹) should he sell the other watch to earn a profit of 18% overall?

The correct option is 13,140.

Step-by-Step Explanation:

Step 1: Find the total cost price of both watches.
The cost price of each watch is ₹9,000.
Total Cost Price (CP) of two watches = 2 × ₹9,000 = ₹18,000.

Step 2: Calculate the required total selling price for an overall profit of 18%.
Overall profit percentage desired = 18%.
Total required Selling Price (SP) = Total CP × (1 + Overall Profit %)
$\text{Total SP}=\mathrm{18,000}\times \left(1+\frac{18}{100}\right)$
$\text{Total SP}=\mathrm{18,000}\times \frac{118}{100}$
$\text{Total SP}=180\times 118=\text{₹}\mathrm{21,240}$

Step 3: Calculate the selling price of the first watch (sold at a 10% loss).
Cost price of the first watch = ₹9,000.
Loss percentage = 10%.
Selling Price of the first watch (SP₁) = CP × (1 - Loss %)
${\text{SP}}_1=\mathrm{9,000}\times \left(1-\frac{10}{100}\right)$
${\text{SP}}_1=\mathrm{9,000}\times \frac{90}{100}$
${\text{SP}}_1=\text{₹}\mathrm{8,100}$

Step 4: Determine the selling price required for the second watch.
Selling Price of the second watch (SP₂) = Total required SP - SP₁
${\text{SP}}_2=\mathrm{21,240}-\mathrm{8,100}=\text{₹}\mathrm{13,140}$

Therefore, the merchant should sell the other watch for ₹13,140 to earn an overall profit of 18%.