**Solution:**

Let's assume the cost price of the goods purchased by the dishonest shopkeeper is 100 units.

**Step 1: Buying Goods**

The shopkeeper defrauds by x% while buying goods. This means he pays only (100 - x)% of the actual cost price to the supplier.

So, the shopkeeper pays (100 - x)% of 100 units, which is (100 - x) units.

**Step 2: Selling Goods**

Now, the dishonest shopkeeper wants to gain x% on the cost price of the goods.

To calculate the selling price, we need to add the desired gain to the cost price.

The desired gain is x% of the cost price, which is (x/100) * 100 units = x units.

Therefore, the selling price of the goods will be the cost price plus the desired gain, which is 100 units + x units = (100 + x) units.

**Step 3: Calculating the Gain Percentage**

To find the gain percentage, we need to calculate the profit earned by the shopkeeper and express it as a percentage of the cost price.

Profit = Selling Price - Cost Price = (100 + x) units - 100 units = x units.

Now, we can calculate the gain percentage using the formula:

Gain Percentage = (Profit/Cost Price) * 100

Substituting the values, we get:

Gain Percentage = (x/100) * 100 = x%

Therefore, the gain percentage on the outlay is x%.

**Explanation:**

The dishonest shopkeeper defrauds both while buying and selling goods. By using faulty weights, he pays less than the actual cost price while buying goods and sells them at a higher selling price to gain a profit.

In this scenario, the dishonest shopkeeper gains x% on the outlay, where x represents the extent of the fraud while buying and selling goods. This gain percentage is obtained by calculating the profit earned and expressing it as a percentage of the cost price.

It is important to note that the gain percentage is directly proportional to the extent of fraud, represented by x%. The higher the value of x, the greater the gain percentage on the outlay.