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# Introduction To Business Mathematics And Statistics Pdf

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Mathematics is an important part of managing business. Business and mathematics go hand in hand this is because business deals with money and money encompasses everything in itself. There is a need for everyone to manage money as some point or the other to take decisions which requires everyone to know mathematics.

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## Business Math: A Step-by-Step Handbook

Example 3 :If again a quantity decreases by a given ratio, then multiply the quantity by the lesser ratio. Example 4 :If both increase and decrease of a quantity are present is a problem, then multiply the quantity by greater ratio for inverse and lesser ratio for decrease, to obtain the final result.

In proportion the first and fourth terms are known as extremes, while second and third terms are known as means. Compound Proportion :If two or more ratios are multiplied together then they are known as compounded. This method is also known as compound rule of three.

Example 5 : 10 men working 8 hours a day can finish a work in 12 days. In how many days can 12 men working 5 hours a day finish the same work.? Example 15 : The prime cost of an article was three times the value of material used. The cost of raw materials was increased in the ratio 3 : 4 and the productive wage was increased in the ratio 4 : 5. The ratio of the present age of a father to that of his son is 5 : 3. Ten years hence the ratio would be 3 : 2. Find their present ages.

The monthly salaries of two persons are in the ratio of 3 : 5. Find the respective salaries. What must be subtracted from each of the numbers 17, 25, 31, 47 so that the remainders may be in proportion. In a certain test, the number of successful candidates was three times than that of unsuccessful candidates. If there had been 16 fewer candidates and if 6 more would have been unsuccessful, the numbers would have been as 2 to 1. Find the number of candidates.

A certain product C is made or two ingredients A and B in the proportion of 2 : 5. The price of A is three times that of B. Find the cost A and B per tonne. The prime cost of an article was three times than the value of materials used.

The cost of raw materials increases in the ratio of 3 : 7 and productive wages as 4 : 9. There has been increment in the wages of labourers in a factory in the ratio of 22 : 25, but there has also been a reduction in the number of labourers in the ratio of 15 : Find out in what ratio the total wage bill of the factory would be increased or decreased. Three spheres of diameters 2, 3 and 4 cms. Find the diameter of the new sphere assuming that the volume of a sphere is proportional to the cube of its diameter.

Note : When quantities x 1 , x 2 ,…. If he engages 20 men and 12 women, the total amount paid per day is 2. The interest is payable yearly, half-yearly, quarterly or monthly. The sum of the principal and interest due at any time, is called the Amount at that time. The rate of interest is the interest charged on one unit of principal for one year and is denoted by i. So here we find four unknown A, P, i. In counting days one of two extreme days is to be excluded, Usually the first day is excluded.

Find the two rates at which he borrowed the amount. Again interest may also be calculated by days. How much interest was due to him on 30th June following? What rate of interest is calculated in the second case?

Taking [Hints. Find the rate of interest charged. A certain sum at a certain rate of interest p. Find the rate percent p. If the amounts repayable by the two banks at the end of 7 years are to be equal.

Find the individual amount of deposit. Hence the principal does not remain same, but increases at the end of each interest period. A year is generally taken as the interest-period, but in most cases it may be half-year or quarter-year. Find the principal and the rate in interest. Now r x. Hence by applying logarithm to the formula of compound interest, the solution becomes easy.

In formula i since P amount to A in years, P may be said to be present value of the sum A due in n years. If any three of the four unknowns A, P, n and i are given, we can find the fourth unknown from the above formula. Find the rate of interest and the sum. Find the sum. Find the CI. What is the rate per cent p. The wear and tear of a machine is taken each year to be one-tenth of the value at the beginning of the year for the first ten years and one-fifteenth each year for the next five years.

Find its scrap value after 15 years. Find the number of years the machine was used. The interval may be either a year or a half-year or, a quarter year or a month.

Definition : Amount of an annuity :Amount of an annuity is the total of all the instalments left unpaid together with the compound interest of each payment for the period it remains unpaid. If the instalments are allowed to accumulate, what will be the total accumulation at the end of 9 years? Then we have 1.

Find how much the accumulations will amount to at the end of 30 years of his for every rupees of his monthly salary. Example 45 :A Professor retires of the age 60 years. What single sum is equivalent to his pension? If the first instalment is paid after six months from the date of purchase, find the amount of each instalment.

He allows his deposits to accumulate with the company at compound rate. Find the amount standing to his credit one year after he has made his yearly investment for the tenth time? Analyse the payments into those on account of interest and an account of amortisation of the principal.

He wants to commute onfourth of his pension to ready money. It is assumed that pension for a year is due at the end of the year. Ani It was discounted on 28 th June. What did the banker pay to the holder of the bill? This is particularly helpful in the settlement of the following types of accounts, viz.

Types of ProblemsTwo types of problems may arise. They are : 1 Where amount is lent in various instalments but repayment is made in one instalment only; 2 Where amount is lent in one instalment but repayment is made in various instalments. Method 1 : Where amount is lent in various instalments but repayment is made in one instalment :Step 1. Take up the starting date' preferably the earliest due date as '0' date or 'base date' or 'starting date' ;Step 2.

Calculate the number of days from '0' date to each of the remaining due dates;Step 3. Multiply each amount by the respective number of days so calculated in order to get the product;Step 4.

Add up the total products separately;Step 5. Divide the total products by the total amounts of the bills;Step 6. Add up the number of days so calculated with '0' date in order to find out the Average or Mean Due Date.

Date of Maturity and CalculationsIf there is an after date bill, the period is to be counted from the date of drawing the bill but when there is any after sight bill, the said period is to be counted from the date of acceptance of the bill. For example, if a bill is drawn on 28th January , and is made payble at one month after date, the due date will be 3rd day after 28th Feb.

To Sum up i When the period of the bill is stated in days, the date of maturity will also be calculated in terms of days i. ## FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Introduction to Probability. Conditional Probability Business and Technical Education Council (National level). Association of require a practical foundation of Mathematical and Statistical techniques used in Business, Commerce.

We provide complete business mathematics notes. Business Mathematics study material includes business mathematics notes , business mathematics book , courses, case study, business mathematics syllabus , question paper, MCQ, questions and answers and available in business mathematics pdf form. Business Mathematics subject is included in B. 