Step 1: Since 10% took a rest, 90% went for either shopping or sightseeing or both.

Step 2: Use the principle of inclusion-exclusion to find the percentage of members who went for both shopping and sightseeing. $|S \cup T| = |S| + |T| - |S \cap T|$

Where: $|S \cup T|$ is the percentage of members who went for either shopping or sightseeing or both (90%). $|S|$ is the percentage of members who went for shopping (80%). $|T|$ is the percentage of members who went for sightseeing (50%). $|S \cap T|$ is the percentage of members who went for both shopping and sightseeing.

Substitute the known values: $90 = 80 + 50 - |S \cap T|$

Solve for $|S \cap T|$: $|S \cap T| = 80 + 50 - 90 = 40$%

Step 3: The percentage of members who went for only shopping is the total percentage who went for shopping minus those who went for both shopping and sightseeing: Only Shopping = $|S| - |S \cap T| = 80\% - 40\% = 40\%$

Statement 1 is correct. Statement 2 is incorrect.