Q.1. Find the mean of the 32 numbers, such that if the mean of 10 of them is 15 and the mean of 20 of them is 11. The last two numbers are 10.

Sure, here is the step by step solution:

Step 1: First, we need to find the sum of the first 10 numbers. We know that the mean is the sum of the numbers divided by the count of the numbers. So, the sum of the first 10 numbers is 10 * 15 = 150.

Step 2: Next, we find the sum of the next 20 numbers. Using the same logic, the sum of these 20 numbers is 20 * 11 = 220.

Step 3: We know that the last two numbers are 10 each, so their sum is 2 * 10 = 20.

Step 4: Now, we add all these sums together to get the total sum of the 32 numbers. So, the total sum is 150 + 220 + 20 = 390.

Step 5: Finally, we find the mean of the 32 numbers by dividing the total sum by the count of the numbers. So, the mean is 390 / 32 = 12.1875.