1. BASICS OF BUSINESS MATHEMATICS by : DR. T.K. JAIN AFTERSCHO ☺ OL centre for social entrepreneurship sivakamu veterinary hospital road bikaner 334001 rajasthan, india www.afterschoool.tk mobile : 91+9414430763

2. THE SUM OF THE DIGITS OF A TWO DIGIT NUMBERS IS 10, IF 18 IS SUBTRACTED FROM IT THE DIGITS IN THE RESULTING NUMBER WILL BE EQUAL ? Options : 37,73,75 SOLVE FROM OPTIONS : 73

3. The 4 th part of a number exceeds the 6 th part by 4, what is the number? Options: 84,44,48 Solve by options : 48 answer

4. 10 years ago the age of father was 4 times his son, 10 years hence, the age of the father will be twice that of his son, what is the present age of them : options : (50,20), (60,20), (55,25) Solve by options : (50,20) answer

5. A number consists of two digits, the digits in 10 th place is 3 times the digit in the unit place, if 54 is subtracted from number, the digits are reversed. Options : (39, 92, 93,94) Solve from options : 93 is answer

6. When a student is asked to divide half of a number by 6, and other half by 4, and then to add two quantities, instead of doing this, he divides the given number by 5, If the answer is 4 short of correct answer, what is the actual number. Options : 320,400,480 Solve by options 480 is answer : 480/5 = 96 240/6 = 40 + 240/4= 60 added= 100 difference = 4 answer

7. If a number of which the half is greater than 1/5 th of the number by 15, then the number is ? options : 50,40,80 Solve by options 50 50 / 5 = 10, half of 50 = 25, difference is 15, so this is answer.

8. Find the fraction, which is equal to half when both its numerator and denominator are increased by 2. it is equal to 3/4 th when both are increased by 12. options : 3/8, 5/8, 2/3 Solve by options : 3/8

9. A number between 10 and 100 is 5 times the sum of its digits. If 9 is added to it, the digits are reversed. Options : 54,53,45,55 Answer = 45

10. The numbers are such that twice the 2nd number exceeds twice the 1st one by 18 and 1/3 rd of smaller and 1/5 th of greater number are together 21. Options : (36,45), (45,36),(50,41)(55,46) Solve by options, answer : 36, 45

11. Sum of the digits in a 3 digit number is 12. If the digits are reversed by the number the number is increased by 495, but reversing only of the ten's and unit digit increases the number by 36, what is it? Options : 327,372,237,273 Solve by options : answer = 237

12. A number consisting of 2 digits is 4 times the sum of its digits and if 27 is added to it, the digits are reversed, the number is ? Options: 63,35,36,60 Answer = 36

13. What is a set? A collection of well defined objects. It is in two types : 1. roster 2. set builder form in roster, we put each item, in set builder form, we put the set in the form of a statement – which denotes how set will be prepared.

14. What is U In set theory U means union, when you add two sets, it is U. A={1,2,3}, B={3,4} AUB={1,2,3,4}

15. A set containing n elements has 2^n subsets There is also an empty set. A {1,2,3,}, can give you 2^3 = 8 subsets, how : 1,2,3, (1,3), (1,2), (2,3), (1,2,3),(empty set) answer

16. What is intersection :? A={1,2,3}, B={3,4} A intersection B={3} it is written as reverse U.

17. What is function? Mapping or function relates two sets. There is a relation between two sets denoted by f, which specifies a relation between elements of two sets.

18. Types of functions... One – one function : A={1,2,3}, B={2,4,6} we can write the relation as f(x)=2x where the relation is from A to B. A={1,2,3} is called domain and B={2,4,6} is called range. f(x) is called relation or function.

19. What is ordered pair? We denote the pairs of elements of domain and range in the form of ordered pair. Example : A={1,2,3}, B={2,4,6} f(x)=2x, here we have 3 ordered pairs : (1,2), (2,4), (3,6) , if we have two ordered pairs starting with the same elements of domains, then this is not a function. Example : (1,2), (1,3) is not a function as the domain element is same. However, two range elements are allowed, ex: (1,2), (2,2) is permitted.

20. What is onto or surjective function? Here we have exactly equal number of elements in domain and range and it is one for one.

21. Denominator of a number is 3 times its numerator. If the ratio of the numbers that are added to the numerator and denominator, is 1:3, find the new fraction that is formed. 1/3 (this is just a question to check your ability to understand the question).

22. The age of a person is twice the sum of the ages of his two sons, 5 years ago his age was thrice sum of their ages. What is his age Options : 60,50,52,51 Try options, answer is 50, double of 25 and trice 15 , 5years ago, fulfills our conditions

23. The wages of 8 men and 6 boys amount to rs. 33 if 4 men earn Rs. 4.5 more than 5 boys, determine the wages of each men and boy? Options (1.5,3) (3,1.5) (2.5,2) (2,2.5) Answer : (3,1.5)

24. 5 times of a positive whole number is 3 less than twice the square of the number, what is the number? Options 3,4,-3,2 Answer = 3

25. The area of rectangle is 2000 sq.cm., its perimeter is 180, what is the length and bredth? Options : (205,80), (50,40) (40,50) Try options : 50, 40, their sum is 90, so perimeter is 180, their area is 2000. Length is always more so 50 is length and 40 bredth.

26. Divide 50 into two parts – sum of the reciprocals of the parts is 1/12. what are the two parts? Options : (24,26), (28,22), (27,23) (20,30) Try options : 20 and 30, add 1/20 and 1/30 = 50/600 = 1/12 so this is the answer.

27. There are 2 consecutive numbers such that the difference of their reciprocals is 1/240, the numbers are ? Options : (15,16), (17,18), (13,14) (12,13) Try 15 and 16 1/15-1/16 = 1/240 answer

28. The sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units respectively, and right angle triangle is formed. The sides of the original triangle was ?options (17,16,15,18) Try 17, you get : 5,4,3,,which make a right angle triangle. 5^2 = 4^2+3^2 answer

29. The sum of 2 irrational numbers multiplied by larger one is 70 and their difference is multiplied by smaller one gives 12, the two numbers are ? Options (3sqrt(2), 2(sqrt(3) ), (5*1.44, 3*2.4) , ( 2*1.44, 5*1.44) Try with options, correct answer is last options : (2*sqrt(2) and 5*sqrt(2) their diference is 4 and their sum is 10, and the numbers are 3 and 7, which fulfill our conditions.

30. The distributor of apple juice has 5000 bottles in the store, it wishes to distribute in a month. From experience it is known that the demand (in number of bottles is given by d=-2000p^2+2000p+17000 price per bottle that will result into zero inventory is ? Options (3,5,2) Put d = 5000, let us try with 3, -2000*9+2000*3+12000 = 0 thus if p=3, we get the answer

31. Effective rate of interest corresponding to a nominal rate 3% per annum payable half yearly is ? Options (3.2, 3.25, 3.0225) Let us assume that we get 20000 amount. After 6 months it will be 20300 after another 6 months, we have interest : 304.5, thus total amount is : 20604.5 thus effective rate of interest is : 3.0225 answer

32. The population of a town increases every year by 2%. In how many years, population will increase by 40%? options : 7,10,17 (1.02)^n = 1.4 at the endof 7 years it is 1.35, but not 1.4 at the end of 8 years we are able to have 40% increase, as we dont have option 8, so answer is 10.

33. A machine the useful life of which is estimated to be 10 years costs 10000, rate of depreciation is 10% per annum, scrap value at the end of the life is ? Options : 3483, 4383, 3400 10000 * (1-.1)^10 = 3483 approx. Answer

34. The annual birth and death rates per thousand are 39.4 and 19.4 respectively, the number of years in which the population will be double assuming there is no immigration or emigration is ? Options : 35, 30, 25 (1.02)^n =2 solve it the answer is 35.

35. If A and B are roots of X^2+7X+12=0, find the equations whose roots are (A+B)^2 and (A-B)^2? Root of the equation are : -3, and – 4 put the value as A and B 49 and 1 new equaltion : x^2 -(sum of roots)X+product of roots = 0 X^2-50X+49 = 0 answer

36. In triangle ABC, angle A and B are in ratio 4:5 and angle B is 30 more than angle C, what are these angles? 4X+5X+(5X-30) = 180 (total of angles is always 180 degrees) 14X = 210 x=210/14 = 15 thus angles A,B,C are : 60, 75, 45 answer

37. The ratio of volumes of two cylinders is X:Y, the ratio of their heights is P:Q, find the ratio of squares of their diameters? pir^2p = X pir^2q=Y divide both the equation by pi, and finding the value of R^2 in each : r = sqrt(X/P) and sqrt (Y/Q) thus the ratio of diameters are (X/P) : (Y/Q)

38. 50 is divided amont 6 men,12women and 17 boys, so that 2 men get as much as 5 boys and 2 women as much as 3 boys, what is the share of each boy? 2M=5B, 3B=2W(equal boys, LCM is 15B) 6M=15B=10W, ratio is : 5:2:3 now multiply by numbers : (5*6) : (2*17): (3*12) = M:B:W= 15:17:18 boys got 17, each boy gets 1. answer

39. An employer reduced number of employees by 1/9, increased their wages by 1/14, what is the ratio of total wages paid to the employee before and after this change? Multiply 9 to 14. Let us assume that total payment in the beginning = 126, now it gets reduced : 126*8/9= 112, now it is increase by 1/14 = 112+8 =120 ratio: 126:120 := 21:20 answer

40. Kapil's expenditure and savings are in the ratio : 4:1, his income increases by 20%, if savings also increase by 12%, by how much % his expenditure has increased? Let us assume income 400 and savings 100, expenditure 300. new income : 480 , new savings : 112, new expenditure : 368, thus it has increased by : 68/300*100 = 22.6% answer

41. An group of 7300 troops is formed in 4 groups so that half of 1 st and 2/3 rd of 2 nd and 3/4 th of 3 rd and 4/5 th of 4 th are equal, how many persons are there in each group? 1/2X=2/3Y=3/4Z=4/5W = 24A (assume) X=48A, Y = 36A, Z=32A, W=30A thus their ratio is : 24:18:16:15 thus 1 st group has 2400, 2 nd group = 1800, 3 rd group = 1600, 4 th group = 1500 answer.

42. THANKS.... GIVE YOUR SUGGESTIONS AND JOIN AFTERSCHOOOL NETWORK / START AFTERSCHOOOL NETWORK IN YOUR CITY [email_address] PGPSE – WORLD'S MOST COMPREHENSIVE PROGRAMME IN SOCIAL ENTREPRENEURSHIP