A shopkeeper bought six identical mobile phones for ₹72,000. He sold two of these mobile phones for ₹42,000. Find his gain percentage.

The correct option is 75%.

Let us break down the problem step-by-step to calculate the shopkeeper's gain percentage.

Step 1: Calculate the cost price of one mobile phone.

The total cost price for 6 identical mobile phones is given as ₹72,000.

Cost price of 1 mobile phone = Total Cost / Number of mobile phones

$\text{Cost price of 1 phone}=\frac{72000}{6}=\text{₹}\mathrm{12,000}$

Step 2: Calculate the cost price of the two mobile phones sold.

Since the shopkeeper sold 2 mobile phones, we find their total cost price:

Cost price of 2 mobile phones = 2 × ₹12,000

$\text{Cost price of 2 phones}=\text{₹}\mathrm{24,000}$

Step 3: Calculate the gain (profit).

The selling price for these 2 mobile phones is given as ₹42,000.

Gain = Selling Price - Cost Price

$\text{Gain}=42000-24000=\text{₹}\mathrm{18,000}$

Step 4: Calculate the gain percentage.

The formula for gain percentage is:

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

Substituting the values into the formula:

$\text{Gain Percentage}=\left(\frac{18000}{24000}\right)\times 100$

Simplify the fraction:

$\frac{18000}{24000}=\frac{3}{4}$

Now, calculate the percentage:

$\text{Gain Percentage}=\frac{3}{4}\times 100=75\%$

Thus, the shopkeeper's gain percentage is 75%.