Quick Solution

This problem can be solved by setting up a system of two algebraic equations based on the two scenarios provided in the question.

1. Set Up the Equations

- Let the actual number of males be M and the actual number of females be F.

• From Scenario 1: "If 15 females are absent (F - 15), then number of males (M) will be half of females."
  This gives us the equation: M = (1/2)(F - 15), which simplifies to 2M = F - 15.
• From Scenario 2: "If 45 males are absent (M - 45), then female strength (F) will be 5 times that of males."
  This gives us the equation: F = 5(M - 45).

2. Solve for the Number of Males (M)

- We have two equations and two variables. The easiest way to solve is to substitute the second equation into the first one to eliminate F:
2M = [ 5(M - 45) ] - 15

- Now, we can solve this single equation for M:
2M = 5M - 225 - 15
2M = 5M - 240
240 = 5M - 2M
240 = 3M
M = 240 / 3 = 80.

3. Verification (Optional)

- If there are 80 males, we can find the number of females using the second equation: F = 5(80 - 45) = 5(35) = 175 females.
- Let's check Scenario 1: If 15 females are absent, there are 175 - 15 = 160 females. Is the number of males (80) half of 160? Yes. The answer holds true.

Final Answer: The number of males actually present is 80.