If the selling price of 16 water bottles is equal to the cost price of 17 water bottles. Find gain per cent percent earned by the dealer.

Answer

To solve the problem, we need to find the gain percent earned by the dealer when the selling price of 16 water bottles is equal to the cost price of 17 water bottles.

Let's denote:
- Cost Price (CP) of one water bottle = x
- Selling Price (SP) of one water bottle = y

From the information given:
The selling price of 16 water bottles is equal to the cost price of 17 water bottles.

This can be expressed mathematically as:
\[ 16y = 17x \]

Now, we can find the selling price of one water bottle in terms of the cost price:
\[ y = \frac{17x}{16} \]

Next, we can calculate the gain:
Gain = Selling Price - Cost Price
\[ \text{Gain} = y - x \]
Substituting the value of y:
\[ \text{Gain} = \frac{17x}{16} - x \]

To simplify this, we need a common denominator:
\[ \text{Gain} = \frac{17x}{16} - \frac{16x}{16} \]
\[ \text{Gain} = \frac{17x - 16x}{16} \]
\[ \text{Gain} = \frac{x}{16} \]

Now, we can calculate the gain percent:
\[ \text{Gain Percent} = \left( \frac{\text{Gain}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Gain Percent} = \left( \frac{\frac{x}{16}}{x} \right) \times 100 \]

The x in the numerator and denominator cancels out:
\[ \text{Gain Percent} = \left( \frac{1}{16} \right) \times 100 \]
\[ \text{Gain Percent} = 6.25\% \]

Thus, the gain percent earned by the dealer is **6.25%**.