To find the population after 3 years given that it increases at a rate of 10% per annum, you can use the formula for exponential growth:

𝑃=𝑃0×(1+𝑟)𝑛P=P0×(1+r)n

Where:

• 𝑃P = Population after 𝑛n years
• 𝑃0P0 = Initial population
• 𝑟r = Rate of increase (in decimal form)
• 𝑛n = Number of years

Given:

• 𝑃0=12,000P0=12,000 (Initial population)
• 𝑟=0.10r=0.10 (10% increase per annum)
• 𝑛=3n=3 (Number of years)

Substitute these values into the formula:

𝑃=12,000×(1+0.10)3P=12,000×(1+0.10)3

𝑃=12,000×(1.10)3P=12,000×(1.10)3

𝑃=12,000×(1.331)P=12,000×(1.331)

𝑃=15,972P=15,972

So, the population after 3 years would be approximately 15,972.

Let's denote the total number of students who appeared in the examination as 𝑥x.

Given that 92% of the students passed, it means 8% failed because the total percentage is 100%.

We can set up the equation:

To find 8% of 𝑥x, we multiply 𝑥x by 81001008 (which is the same as multiplying by 0.08):

Now, we can solve for 𝑥x:

So, 6000 students appeared in the examination.