JAGANNATH INSTITUTE OF MANAGEMENT SCIENCES BUSINESS MATHEMATICS II BBA- 2 ND SEMESTER (Code -205)

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1 JAGANNATH INSTITUTE OF MANAGEMENT SCIENCES BUSINESS MATHEMATICS II BBA- 2 ND SEMESTER (Code -205) UNIT-1 SCOPE AND IMPORTANCE OF BUSINESS MATHS : Mathematics is an important subject and knowledge of it enhances a person s reasoning, problem solving skills. Hence, it is important for understanding every subject whether it is science and technology,medicine, economy, business or finance.mathematical tools such as theory of chaos are used to mapping market trends and forecasting of the same.statistics and probability which are branches of mathematics are used in everyday business and economics.maths also form an important part of accounting. The role of mathematics in business is very important in the process of managerial decision models and algorithms. IMPORTANT FACTS AND FORMULAE ON PROFIT AND LOSS Cost Price (C.P) : The price at which an article is purchased is called its cost price. Selling Price (S.P) : The price at which an article is sold is called its selling price.

2 Profit or Gain : If S.P is greater than C.P,the seller is said to have a profit. Loss : If S.P is less than C.P,the seller is said to have incurred a loss. 1. Gain = S.P C.P (Rs) 2. Loss = C.P S.P (Rs) 3. Gain or Loss is always calculated on C.P 4. Gain (%) = x Loss (%) = x S.P = x C.P 7. S.P = x C.P 8. C.P = S.P 9. C.P = x S.P 10. If an article is sold at a gain of 35 % (say), then S.P = 135% of C.P 11. If an article is sold at a loss of 35 % (say), then S.P = 65% of C.P

3 12. When there are two successive profits of x% and y % then the resultant profit% is given by x + y When there is a profit of x% and loss of y% in a transaction,then the resultant profit or loss percent is given by x y - ve sign respectively., according to the +ve or SOME IMPORTANT SOLVED QUESTIONS Q If a man purchases 11 oranges for Rs 10 and sells 10 oranges Rs 11.How much profit or loss does he make? Soln : Suppose the man bought 11 x 10 = 110 oranges C.P of 11 oranges = Rs C.P,, 1,, = Rs 10 C.P,, 110,, = Rs 10 x 110 = Rs Similarly, S.P of 110 oranges = Rs 121 Profit = Rs ( S.P - C.P ) = Rs ( ) = Rs 21

4 Profit % = Profit x 100 = 12 x 100 = 21% CP 100 Quicker method : Ans : 21% ************************ Purchases 11 oranges for Rs 10 Sells 10 oranges for Rs 11 Profit % = 11 x x 10 x 100 = 21 % 10 x 10 ****************** Q A man bought a cycle for Rs 250.For how much should he sell so as to gain 10%? Soln: If C.P is Rs 100, S.P = Rs 110,,,,,, Re 1,,, = Rs,,,,,, Rs 250,,, = Rs x 250 = Rs 275 Ans : Rs 275 Q By selling a horse for Rs 570, a trader would lose 5 %.At what price must he sell it so as to gain 5 %?

5 Soln : ( ) % = 95% of the C.P = Rs 570 1%,,,,,, = Rs Rs 630 ( ) % = 105%,,,,,, = Rs x 105 = Ans : Rs 630 *************************** Q A machine is sold for Rs 5060 at a gain of 10 %.What would have been the gain or loss % if it had been sold for Rs 4370? Soln: We know C.P = Rs x S.P = Rs x 5060 = Rs nd S.P = Rs 4370 Loss = Rs ( C.P - S.P ) = Rs ( ) = Rs 230 Loss (%) = x 100 = x 100 = 5 % Ans : 5 % ***********************

6 IMPORTANT FACTS AND FORMULAE ON SIMPLE AND COMPOUND INTEREST 1. Interest is the money paid by the borrower to the lender for the use of money lent. 2. The sum lent is called is called the principal. 3. Interest is usually calculated at the rate of so many rupees for every Rs 100 for the money lent for a year.this is called rate % per annum. 4. Per annum means for a year 5. The sum of the principal and interest is called the amount 6. The interest is usually paid yearly,half-yearly or quarterly as agreed upon. 7. Interests are of two kinds - Simple and Compound Interest 8. When interest is calculated on the original principal for any length of time,it is called Simple Interest (S.I) For e.g S.I on Rs 100 at 5% per annum will be Rs 5 each year,i.e at the end of 1 yr total amount will be Rs 105, at the end of 2 nd year, it will be Rs 110 and so on.

7 9. When interest is calculated on the amount on the previous year, then it is called Compound Interest.(C.I) For e.g interest on Rs 100 at 5 % per annum compound interest at the end of 1 st year is Rs 5, at the end of 2 nd yr is Rs 5.25, at the end of 3 rd yr will be Rs and so on. 10. P = principal, t = time, r = rate %, A = amount S.I = P x t x r A = P + S.I 12. P = S.I x 100 t x r 13. Rate = S.I x 100 P x t 14. Time = S.I x P x r 15. When interest is compounded annually A = P, C.I = A - P 16. When interest is compounded half-yearly A = P 17. When interest is compounded quarterly A = P 18. When the rate of interest is r %, r % and r % for the 1 st, 2 nd and 3 rd year

8 respectively,then A = P SOME SOLVED QUESTIONS Q What sum of money placed at S.I at 4% will yield Rs 50/ interest in 6 months? Soln: By the question, S.I = Rs 50 / Rate r = 4 % Time t = 6 months = 6/12 = 1/2 yr Principal P =? We know, P = S.I x 100 = 50 x 100 x 2 = Rs 2500 t x r 4 Ans : Rs 2500 ***************************** Q How long will it take Rs 3000 to amount to Rs 3300 at 4% S.I? Soln: P = Rs 3000/ A = Rs 3300 / S.I = A - P = Rs ( ) = Rs 300 r = 4% T =? We know, T = S.I x 100 = 300 x 100 = 2.5 yrs P x r 3000 x 4

9 Ans : 2.5 yrs ************************** Q. A man lent Rs 10,000/- to two persons in two parts. The first man borrowed at 5% & the second person borrowed at 6 % interest per annum. If he receives Rs 12,240/ as total amount after 4 years then what sum was borrowed by each of the two persons? Soln : Principal P = Rs 10,000 Let the 1 st man borrow Rs X Then the 2 nd man borrows Rs ( X) Both the man borrowed the amount for 4 years A = P + S. I = S.I S.I = Rs 2240 For the 1 st man, S.I = X x 4 x 5 = 20 X = X For the 2 nd man, S.I = ( X ) x 4 x 6 = 6 ( X ) Now, X + 6 ( X ) =

10 5X X = 2240 x 25 X = = 4000 Therefore, the 1 st man borrowed Rs 4000 And the 2 nd man borrowed Rs 6000 Ans : Rs 4000 ; Rs 6000 Q. A certain sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself? Soln: Suppose the sum be Rs P Amount A = Rs 2P Time = 12 years We know, A = P r t or, 2P = P r or, 2 = 4 r r 12 Cubing both sides, 8 = r 12 or, 8P = P Hence, the required time is 12 years. Ans : 12 years **********************************

11 Q. A certain sum of money is put invested at 4% C.I for 2 yrs at 20% per annum. The interest for the 2 nd year is Rs 25.Find the interest for the 3 rd year? Soln: Let P be the original sum which is invested at 4 % compounded annually. So,we have Principal = P Time t = 2 yrs Rate r = 4% We have, A = P = P (1.04) 2,which is the amount at the end of 2 nd year. Amount at the end of 3 rd year = P (1.04) 3 Interest for the 2 nd = P (1.04) 2 - P ( 1.04) or, 25 = P (1.04) 2 - P ( 1.04) (given) or, 25 = P (1.04) ( ) or, 25 = P (1.04) (0.04) (1) Interest for the 3 rd year = P (1.04) 3 - P (1.04) 2 = P (1.04) 2 ( ) = P (1.04) 2 (0.04) = 25 x 1.04 ( from (1) ) = Rs 26 Ans : Rs 26 ****************************

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