Let the total amount of money be $T$, and let the number of people be $n$. We are given two conditions:

1. If there had been 4 more people, everyone would have received Tk 16 less.
2. If there had been 4 fewer people, everyone would have received Tk 24 more.

Let's express these conditions mathematically:

1. The amount each person receives normally is $\frac{T}{n}$.

2. If there were 4 more people, each person would receive $\frac{T}{n+4}$. According to the first condition, this is Tk 16 less than $\frac{T}{n}$, so we can write the equation: $\frac{T}{n} - \frac{T}{n+4} = 16$

3. If there were 4 fewer people, each person would receive $\frac{T}{n-4}$. According to the second condition, this is Tk 24 more than $\frac{T}{n}$, so we can write the equation: $\frac{T}{n-4} - \frac{T}{n} = 24$

Now we solve this system of equations step by step.

Step 1: Solve the first equation

The first equation is: $\frac{T}{n} - \frac{T}{n+4} = 16$ Multiply both sides by $n(n+4)$ to eliminate the denominators: $T(n+4) - Tn = 16n(n+4)$ Simplify: $Tn + 4T - Tn = 16n(n+4)$ $4T = 16n(n+4)$ Solve for $T$: $T = 4n(n+4)$ So, $T = 4n^2 + 16n$.

Step 2: Solve the second equation

The second equation is: $\frac{T}{n-4} - \frac{T}{n} = 24$ Multiply both sides by $n(n-4)$ to eliminate the denominators: $Tn - T(n-4) = 24n(n-4)$ Simplify: $Tn - Tn + 4T = 24n(n-4)$ $4T = 24n(n-4)$ Solve for $T$: $T = 6n(n-4)$ So, $T = 6n^2 - 24n$.

Step 3: Set the two expressions for $T$ equal

Now we have two expressions for $T$: $4n^2 + 16n = 6n^2 - 24n$ Simplify this equation: $0 = 6n^2 - 24n - 4n^2 - 16n$ $0 = 2n^2 - 40n$ Factor out $2n$: $0 = 2n(n - 20)$ So, $n = 0$ or $n = 20$.

Since the number of people cannot be zero, we have $n = 20$.

Conclusion:

There were 20 people in the group.

Would you like more details or explanations on any step? Here are some related questions you might find interesting:

1. How would the solution change if the amount of money received was different?
2. What if there were 5 fewer or 5 more people instead of 4?
3. Can you apply a similar method for different amounts of money reductions or increases?
4. How would this problem change if we knew the total amount $T$ upfront?
5. How can we generalize this problem for any change in the number of people?

Tip: Always start by expressing each condition as a mathematical equation to simplify solving problems with multiple unknowns.