# Blog

• ### Increase and Decrease in Ratio

If the number of teachers in a college is increased from 50 to 60. Then the ratio of new staff and old staff is   We say that, number of teachers has been increased in ratio 6 : 5. In other words, no. of new staff is times the no. of old staff. Hence Rule: […]

• ### Introduction to Linear Programming

Due to the increasing complexity of business organizations, the role of the management executive as a decision maker is becoming more and more difficult. During the last thirty years or so several statistical and mathematical techniques have been developed in order to meet this situation. It may be observed that certain problems facing the business […]

• ### Inequality and Compound Inequality

Inequality: An inequality expresses the relative order of two mathematical expressions. The symbols (less than), (less than or equal to), (greater than), (greater than or equal to) are used to write inequalities. Note: The sign of an inequality is unchanged if it is multiplied or divided by a positive number, For example, Similarly, Note: The […]

• ### Examples of Inequality and Compound Inequality

Example: Solve and graph the solution of the inequality Solution: We have Thus, the solution set is Solution Set The graph of the solution set. Example: Solve and graph the solution of the inequality . Solution: We have Here equality is not possible, because 13 is always greater than 12, in . So, the solution […]

• ### Linear Inequalities in Two Variables

The inequalities of the form , , , where , , c are constants, are called the linear inequalities in two variable. The points which satisfy the linear inequality in two variable ‘x’ and ‘y’ from its solution. Graphing the Solution Region of Linear Inequality in Two Variables: Example: Graph the solution set of the […]

• ### Examples of Linear Inequalities in Two Variables

Example: Graph the solution set of the system of linear inequalities Solution: We have The corresponding equations of inequalities (A) and (B) For x – intercept For x – intercept Put in (1) we get Put in (2) we get For y – intercept For y – intercept Put in (1) we get Put in […]

• ### Graphing the Solution Region of System of Linear Inequalities

Example: Graph the solution set of the system of linear inequalities. Solution: We have The corresponding equations of inequalities (A), (B) and (C), we get For x–Intercepts: Put in Eq (1), Eq (2) and Eq (3) we get For y–Intercepts: Put in Eq (1), Eq (2) and Eq (3) we get Test: Put origin as […]

• ### Feasible Solution Set

Corner Point OR Vertex: A point of a solution region where two of its boundary lines intersect is called a corner point or vertex of the solution region. Problem Constraint: In a certain problem from everyday life each linear inequality concerning the problem is called the problem constraint. Non – Negative Constraint OR Decision Variables: […]

• ### Concept of Compound Interest

When the interest is calculated for every period on the total previous amount, then the total amount of interest gained on all the periods is called compound interest. Let       Principal = P             Rate of interest = r             No. of years = n             After 1st year, interest                 After 1st year, Amount   […]

• ### Examples of Compound Interest

Example 01: Find the compound amount and compound interest on the principal 20,000 borrowed at 6% compounded annually for 3 years. Solution: Let P = 20000, r = 6%, n = 3 using formula Compound interest Example 02: Find the compound amount, which would be obtained from an interest of Rs.2000 at 6% compounded quarterly […]

• ### More Examples of Compound Interest

To Find Principal We are given n, A, and r We have to find P by the formula Example 01: Find principal, when compound interest for 4 years at 6% is 525. Solution: Let Principal = P, , r = 6%, C.I = 525 We know that To Find Rate When P, n, A are […]

• ### Concept of Simple Interest

When interest is calculated for every period only on the principal, then the total amount of interest gain on all the periods is called simple interest. Let Principal amount = P Rate of interest = r Then amount of interest after one year = Pr. Amount after two years Amount after three years and so […]