- 1. BASICS OF BUSINESS MATHEMATICSby :DR. T.K. JAIN AFTERSCHO
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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 thpart of a
number exceeds the 6 thpart by 4, what is the number? Options:
84,44,48 Solve by options :48 answer 4. 10 years ago the age of
father was4 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 thplace
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 : 320,400,480Solve by options 480 is answer :480/5
= 96 240/6 = 40 + 240/4= 60 added= 100difference = 4 answer 7. If a
number of which the half is greater than 1/5 thof the number by 15,
then the number is? options : 50,40,80Solve 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. itis equal to 3/4 thwhen both are
increased by 12. options : 3/8, 5/8, 2/3Solve 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 rdof smaller and 1/5 thof 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: 63,35,36,60Answer = 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 subsetsThere 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, whichspecifies 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 ofdomain 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 ageOptions : 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? Options3,4,-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 bottlethatwill result into zero inventory is ? Options
(3,5,2)Put d = 5000,let us try with 3,-2000*9+2000*3+12000 = 0thus
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 be20300 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 = 1.4at 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
=2solve 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 4put the value as A and
B 49 and 1new equaltion :x^2 -(sum of roots)X+product of roots =
0X^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 = Xpir^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 stand 2/3 rdof 2 ndand 3/4 thof 3 rdand 4/5 thof 4
thare 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 stgroup has 2400, 2
ndgroup = 1800, 3 rdgroup = 1600, 4 thgroup = 1500 answer. 42.
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