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The mathematical questions in the competitive exams deal with important facts and formulas. They are part of the assessment of the candidate with the use of quantitative tests. So they are known as quantitative aptitude. These tests provide insight into the calculating ability, quick decision-making, and good mathematical knowledge of the candidates. The facts and formulas are mostly from arithmetic and they contain topics like average, sum, fraction, decimal number, percentage, age of people, the relationship between family members, simple interest and complex interest, etc.
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Average
To calculate the average of several numbers, you have to add the numbers and divide their sum by the number of digits you are adding. For example, to calculate the average of a, b, and c, you have to add them and then divide the sum by 3. Average of a, b and c = ( a + b + c ) / 3
Percentage
To calculate the percentage, you have to multiply the decimal number by 100. For example, if x and y are two numbers, then x is ( x / y ) x 100 percent of y and y is ( y / x ) x 100 percent of x.
If you have to calculate the difference, then you have to subtract one number from another. If x and y are two numbers and y is larger than x, then x is { ( y – x ) / x } x 100 lesser than y and y is { ( y – x ) / y } x 100 percent greater than x.
Profit and loss
When the selling price is more than the cost price then a profit has been made and when the selling price is less than the cost price then a loss has been made.
To calculate profit, you have to subtract the cost price from the selling price, and to calculate loss you have to subtract the cost price from the selling price.
Profit = S. P. – C. P., Loss = C. P. – S. P.
To calculate the percentage of profit you have to divide the profit by the cost price and then multiply it by 100.
Percentage of profit = { (S. P. – C. P. ) / C. P. } X 100.
To calculate the percentage of loss you have to divide the loss by the cost price and then multiply it with 100
Percentage of loss = { (C. P. – S. P. ) / C. P. } X 100.
To find out the percentage of profit or loss on an amount for transactions more than once, the formula is + / — x + / — y + / — x.y / 100
Simple Interest
To calculate the simple interest you have to multiply the principal capital with the rate of interest, the given period, and divide it by 100.
If the capital is denoted by A, the rate of interest is denoted by B, the given period is denoted by C and simple Interest is denoted by D, then D = ( A X B X C ) / 100
If the period is given in months then it will need to be converted into a year by dividing it by 12. For example, 6 months = 6 / 12 year = 1 / 2 year
Compound interest
To calculate compound interest, the formula is A = { 1 + ( r / 100 ) }n, where A is the total principal capital with the interest, r is the rate of interest given on the capital, n is the number of years when the capital is being compounded.
When the interest has to be found out, the principal capital has to be subtracted from the increased principal capital.
Age
To calculate the age of the father or the age of the son, when the average of their age and the ratio are given, you have to calculate the sum of the age from the average and then use proportion to calculate the age. For example, if the average age of the father and the son is 30 years and the ratio of their age is 2 : 3, then the sum of their ages is 30 X 2 = 60 years. The equation will be 2 / 5 = son’s age / 60
Son’s age = 60 X 2 / 5 = 24 , father’s age = 60 – 24 = 36
Father’s age can also be found by proportion, 3 / 5 = father’s age / 60
So father’s age = 60 X 3 / 5 = 36
Conclusion
The formulas and shortcuts mentioned here can only provide a preliminary knowledge of mathematical calculation. It is important to know about the background of those formulas and how they are conceived and how they operate. It is also important to know about alternative methods and formulas in these mathematical questions to solve different types of problems.
