Algebraic Representation:

Let's assume that Sangeeta has x number of socks and y number of handkerchiefs. According to the given information,

x + y = 40 ----(1)

When she has 5 less handkerchiefs and 5 more socks,

x + (y - 5) = 4(y - 5) ----(2)

Solving equations (1) and (2) simultaneously will give us the value of x and y.

Graphical Representation:

We can create a graph using the above equations to represent the situation. To plot the graph, we need to rearrange the equation (2) in terms of x, which gives us:

x = 3y - 5

Now, we can plot the two equations on the same graph. The x and y-intercepts of equation (1) are (40,0) and (0,40) respectively. For equation (2), we can plot the intercept at x = 3(-5) = -15, y = -5 and another point at x = 3(35) - 5 = 100, y = 35.

The graph will have two lines intersecting at a point, which represents the solution to the equations.

Explanation:

The problem involves finding the number of socks and handkerchiefs Sangeeta has, given that the total number of items is 40. The second part of the problem involves finding the new number of socks and handkerchiefs when she has 5 less handkerchiefs and 5 more socks, and the socks become 4 times the number of handkerchiefs.

To represent this situation algebraically, we can use two equations, one representing the total number of items, and the other representing the new number of socks and handkerchiefs. Solving these equations simultaneously will give us the values of x and y.

To represent the situation graphically, we can plot the two equations on the same graph and find the point of intersection, which represents the solution to the equations.

Overall, the problem involves using algebraic and graphical methods to find the solution to a situation involving socks and handkerchiefs.