The average weight of the first thirteen persons among fourteen persons is 78 kg. The weight of the 14th person is 39 kg more than the average weight of all the fourteen persons. Find the weight of the 14th person.

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**Solution:**

1. Let the average weight of all 14 persons be *x* kg.

2. Given:
   - Average weight of first 13 persons = 78 kg
   - Weight of 14th person = *x* + 39 kg

3. Total weight of first 13 persons = $13 	imes 78 = 1014$ kg

4. Total weight of all 14 persons = $14x$ kg

5. Sum of weights of first 13 persons and 14th person:
   $$1014 + (x + 39) = 14x$$

6. Simplify the equation:
   $$1014 + x + 39 = 14x$$
   $$1053 + x = 14x$$
   $$1053 = 14x - x = 13x$$
   $$x = \frac{1053}{13} = 81$$

7. Weight of 14th person = $x + 39 = 81 + 39 = 120$ kg

**Answer:** 120 kg

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