A shopkeeper bought six identical mobile phones for ₹45,000. He sold two of these mobile phones for ₹42,000. Find his gain percentage.

The correct option is 180%.

To find the gain percentage, we first need to determine the cost price (CP) of the two mobile phones that were sold, and then compare it with their selling price (SP).

Step 1: Calculate the Cost Price (CP) of a single mobile phone
The shopkeeper bought six identical mobile phones for ₹45,000.

$\text{Cost Price of 1 phone}=\frac{\mathrm{45,000}}{6}=₹\mathrm{7,500}$

Step 2: Calculate the Cost Price (CP) of two mobile phones
Since he sold two of these phones, we find their combined cost price:

$\text{Cost Price of 2 phones}=2\times \mathrm{7,500}=₹\mathrm{15,000}$

Step 3: Find the Gain (Profit) on the two mobile phones
The selling price (SP) of these two mobile phones is ₹42,000. The gain is calculated as:

$\text{Gain}=\text{Selling Price}-\text{Cost Price}$

$\text{Gain}=\mathrm{42,000}-\mathrm{15,000}=₹\mathrm{27,000}$

Step 4: Calculate the Gain Percentage
The gain percentage is calculated relative to the Cost Price of the two phones:

$\text{Gain Percentage}=\left(\frac{\text{Gain}}{\text{Cost Price of 2 phones}}\right)\times 100$

$\text{Gain Percentage}=\left(\frac{\mathrm{27,000}}{\mathrm{15,000}}\right)\times 100$

$\text{Gain Percentage}=1.8\times 100=180\%$

Thus, the shopkeeper's gain percentage is 180%.