Oranges are bought at 6 for Rs. 20 and sold at 4 for Rs. 18. Find the gain or loss per cent.

Answer

To find the gain or loss percentage in this problem, we will follow these steps:

### Step 1: Calculate the Cost Price (CP) of 1 Orange
We know that 6 oranges are bought for Rs. 20. Therefore, the cost price of 1 orange can be calculated as follows:

\[ \text{Cost Price of 1 Orange} = \frac{20}{6} = \frac{10}{3} \text{ Rs.} \]

### Step 2: Calculate the Selling Price (SP) of 1 Orange
Next, we know that 4 oranges are sold for Rs. 18. Therefore, the selling price of 1 orange can be calculated as follows:

\[ \text{Selling Price of 1 Orange} = \frac{18}{4} = \frac{9}{2} \text{ Rs.} \]

### Step 3: Determine the Gain or Loss
Now, we need to find out if there is a gain or loss by comparing the selling price and the cost price.

\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} = \frac{9}{2} - \frac{10}{3} \]

To perform this subtraction, we need a common denominator. The least common multiple of 2 and 3 is 6.

Converting both fractions to have a denominator of 6:

\[ \frac{9}{2} = \frac{27}{6} \quad \text{and} \quad \frac{10}{3} = \frac{20}{6} \]

Now, we can subtract:

\[ \text{Gain} = \frac{27}{6} - \frac{20}{6} = \frac{7}{6} \text{ Rs.} \]

### Step 4: Calculate the Gain Percentage
To find the gain percentage, we use the formula:

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

Substituting the values we have:

\[ \text{Gain Percentage} = \left( \frac{\frac{7}{6}}{\frac{10}{3}} \right) \times 100 \]

To simplify this, we multiply by the reciprocal of the cost price:

\[ \text{Gain Percentage} = \left( \frac{7}{6} \times \frac{3}{10} \right) \times 100 = \left( \frac{21}{60} \right) \times 100 \]

Calculating this gives:

\[ \text{Gain Percentage} = \frac{21 \times 100}{60} = 35\% \]

### Final Answer
The gain percentage is **35%**.

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