One has to run 250 metres to take one round of a ground. A girl has run 75000 centimetres. Then how many rounds has she taken and how many rounds more will she have to take in order to complete a run of 3 kilometres ?

Question

Accepted Answer

To determine how many rounds the girl has taken and how many more she needs to complete a total of 3 kilometers, we need to follow these steps:

1. **Convert the distance run by the girl from centimeters to meters:**
   - The girl has run 75000 centimeters.
   - Since 1 meter = 100 centimeters, we convert 75000 centimeters to meters by dividing by 100.
   - $ 75000 \, \text{cm} = \frac{75000}{100} = 750 \, \text{meters} $.

2. **Calculate the number of rounds she has already completed:**
   - One round of the ground is 250 meters.
   - To find out how many rounds she has completed, divide the distance she has run by the distance of one round.
   - $ \frac{750 \, \text{meters}}{250 \, \text{meters/round}} = 3 \, \text{rounds} $.

3. **Determine the total number of rounds needed to complete 3 kilometers:**
   - First, convert 3 kilometers to meters: $ 3 \, \text{km} = 3000 \, \text{meters} $.
   - Calculate the total number of rounds needed to run 3000 meters.
   - $ \frac{3000 \, \text{meters}}{250 \, \text{meters/round}} = 12 \, \text{rounds} $.

4. **Calculate how many more rounds she needs to take:**
   - She has already completed 3 rounds.
   - To find out how many more rounds she needs, subtract the rounds she has completed from the total rounds required.
   - $ 12 \, \text{rounds} - 3 \, \text{rounds} = 9 \, \text{rounds} $.

Therefore, the girl has taken 3 rounds and needs to take 9 more rounds to complete a run of 3 kilometers. This supports Option 1 as the correct answer: 3,9.

**Explanation of why other options are incorrect:**

- **Option 2 (30,90):** This suggests that the girl has completed 30 rounds and needs 90 more, which is incorrect because she has only run 750 meters, equating to 3 rounds, not 30.
  
- **Option 3 (3,90):** While the first part of this option is correct (3 rounds completed), the second part is incorrect because she only needs 9 more rounds, not 90, to complete 3 kilometers.

- **Option 4 (30,9):** This option incorrectly states that she has completed 30 rounds, which is not possible given the distance she has run (750 meters). The second part (9 more rounds) is correct, but the first part makes this option incorrect overall.

Thus, Option 1 is the correct answer, as it accurately reflects the number of rounds completed and the number of additional rounds needed.