A shopkeeper buys oranges at the rate of 10 oranges for ₹50 and sells them at the rate of 12 oranges for ₹74. Find his gain or loss percentage.

The correct option is 23$\frac{1}{3}$% gain.

Step 1: Find the Cost Price (CP) of 1 orange

The shopkeeper buys 10 oranges for ₹50.

CP of 1 orange = ₹$\frac{50}{10}$ = ₹5

Step 2: Find the Selling Price (SP) of 1 orange

The shopkeeper sells 12 oranges for ₹74.

SP of 1 orange = ₹$\frac{74}{12}$ = ₹$\frac{37}{6}$

Step 3: Determine Gain or Loss

Since the Selling Price per orange ($\frac{37}{6}$ ≈ ₹6.17) is greater than the Cost Price per orange (₹5), the shopkeeper earns a gain.

Gain per orange = SP - CP

Gain = $\frac{37}{6}$ - 5

Gain = $\frac{37-30}{6}$ = $\frac{7}{6}$

Step 4: Calculate the Gain Percentage

The formula for gain percentage is:

Gain % = $\left(\frac{\text{Gain}}{\text{CP}}\right)\times 100$

Substituting the values into the formula:

Gain % = $\left(\frac{\frac{7}{6}}{5}\right)\times 100$

Gain % = $\frac{7}{30}\times 100$

Gain % = $\frac{70}{3}$%

Converting the improper fraction $\frac{70}{3}$% to a mixed fraction:

$\frac{70}{3}$ = 23$\frac{1}{3}$%

Thus, the shopkeeper's gain percentage is 23$\frac{1}{3}$% gain.