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The image contains the following question:

"In the election for the post of Mohanty Tealvya, 50% of the voters favored Progress; the rest favored MMS. But after a few days, 20% of Progress supporters shifted their support to MMS, and 10% of MMS supporters shifted to Progress. What is the minimum percentage of the total votes that Progress must attract in order to tie with MMS?

Options:  
(1) 2.5%  
(2) 8%  
(3) 5%  
(4) 10%"

### Solution:

Let’s denote:
- \( P_0 = 50\% \) of total voters initially supported Progress.
- \( M_0 = 50\% \) of total voters initially supported MMS.
- After the shift, 20% of Progress supporters moved to MMS.
- After the shift, 10% of MMS supporters moved to Progress.

The calculation can proceed as follows:

1. **Shift from Progress to MMS:**
   - 20% of Progress supporters shift to MMS. This is \( 0.2 \times 50\% = 10\% \).

2. **Shift from MMS to Progress:**
   - 10% of MMS supporters shift to Progress. This is \( 0.1 \times 50\% = 5\% \).

After the shifts:
- **Progress's final support** becomes \( 50\% - 10\% + 5\% = 45\% \).
- **MMS's final support** becomes \( 50\% + 10\% - 5\% = 55\% \).

In order for Progress to tie with MMS, Progress must attract enough votes to make both percentages equal. Currently, MMS leads by \( 55\% - 45\% = 10\% \).

Thus, Progress needs to attract an additional **5%** of the total votes to tie with MMS.

### Correct answer:  
**Option (3): 5%**

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Would you like more details or have any questions?

### Related Questions:
1. How would the result change if 30% of Progress supporters shifted to MMS?
2. What if 15% of MMS supporters shifted to Progress instead of 10%?
3. How do you calculate the percentage of votes required to win rather than tie?
4. Can this method be applied to real-life elections?
5. How would the result change if Progress initially had 40% of the votes?

### Tip:  
Always double-check the shifts and percentages, as small miscalculations can lead to significant differences in the final results.

In the election for the post of Mohanty Tealvya, 50% of the voters favored Progress; the rest favored MMS. But after a few days, 20% of Progress supporters shifted their support to MMS, and 10% of MMS supporters shifted to Progress. What is the minimum percentage of the total votes that Progress must attract in order to tie with MMS?
Options:
(1) 2.5%
(2) 8%
(3) 5%
(4) 10%

Learn how to calculate the minimum percentage of votes Progress must attract to tie with MMS, given a shift in voter support. This problem involves percentage calculations and basic algebra concepts. Suitable for Grades 7-9.

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