By increasing the cost of entry ticket to a fair in the ratio `10 : 13`, the number of visitors to the fair has decreased in the ratio `6 : 5`. In what ratio has the total collection increased or decreased ?

Answer

To solve the problem, we need to determine the ratio of the total collection before and after the changes in ticket price and number of visitors.

### Step-by-Step Solution:

1. **Define Variables for Ticket Price and Visitors:**
- Let the initial cost of the entry ticket be \(10x\).
- Let the present cost of the entry ticket be \(13x\).
- Let the initial number of visitors be \(6y\).
- Let the present number of visitors be \(5y\).

2. **Calculate Initial Total Collection:**
- The initial total collection can be calculated as:
\[ \text{Initial Total Collection} = \text{Cost of Ticket} \times \text{Number of Visitors} = 10x \times 6y = 60xy \]

3. **Calculate Present Total Collection:**
- The present total collection can be calculated as:
\[ \text{Present Total Collection} = \text{Cost of Ticket} \times \text{Number of Visitors} = 13x \times 5y = 65xy \]

4. **Find the Ratio of Total Collections:**
- The ratio of the initial total collection to the present total collection is:
\[ \text{Ratio} = \frac{\text{Initial Total Collection}}{\text{Present Total Collection}} = \frac{60xy}{65xy} \]
- Simplifying this gives:
\[ \text{Ratio} = \frac{60}{65} = \frac{12}{13} \]

5. **Interpret the Result:**
- This means that the total collection has increased in the ratio of \(12:13\).

### Final Answer:
The total collection has increased in the ratio of \(12:13\).