Read the given information carefully and answer the related questions:

Seven persons – A, B, C, D, E, F, and G – participate in different activities in seven different months of the same year: January, April, May, July, September, October, and November. The activities are Cooking, Gardening, Photography, Painting, Swimming, Sculpting, and Writing. Gardening is done in a month having 30 days. Three persons perform their activities between D and the one who does Gardening. One person performs their activity between D and E. The number of persons performing activities after E is the same as the number of persons performing activities before the one who does Painting. F performs their activity immediately before the one who does Photography. More than three persons perform their activities between F and G, who does Writing. Swimming is done in a month having 30 days before D. Cooking is done before C, who does not do Swimming.

E performs Painting in the month of _____.

The correct answer is July.

Let us determine the correct month by analyzing the given information step-by-step.

First, arrange the seven months in chronological order along with the number of days in each month:
1. January (31 days)
2. April (30 days)
3. May (31 days)
4. July (31 days)
5. September (30 days)
6. October (31 days)
7. November (30 days)

According to the clues, the number of persons performing activities after E is the same as the number of persons performing activities before the one who does Painting. Since E performs Painting, let E be placed at position

$k$

The number of persons performing activities after E is:

$7-k$

The number of persons performing activities before the one who does Painting (E) is:

$k-1$

Equating the two expressions:

$7-k=k-1$

$2k=8\Rightarrow k=4$

Position 4 corresponds to the month of July. Thus, E performs Painting in the month of July.

We can verify the full schedule for consistency:
• One person performs between D and E (July, position 4). So D can be in April (position 2) or October (position 6).
• Three persons perform between D and the person who does Gardening (in a 30-day month). If D is in October, Gardening is in April (30 days). If D were in April, Gardening would fall in October (31 days), which is invalid. Hence, D is in October and Gardening is in April.
• Swimming is done in a 30-day month before D (October). The 30-day months before October are April and September. Since April is Gardening, Swimming is done in September.
• F performs immediately before Photography. October (F) and November (Photography) are the only available consecutive months.
• More than 3 persons perform between F (October) and G (who does Writing), so G performs in January.
• Cooking is done before C, placing Cooking in May and Sculpting in October.

The completed schedule is as follows:
1. January (31 days): G – Writing
2. April (30 days): Gardening
3. May (31 days): Cooking
4. July (31 days): E – Painting
5. September (30 days): Swimming
6. October (31 days): F / D – Sculpting
7. November (30 days): Photography

Therefore, E performs Painting in the month of July.