MTH302 Business Mathematics mid term paper 2011

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MIDTERM EXAMINATION
Fall 2009
MTH302- Business Mathematics & Statistics (Session - 3)
Ref No:
Time: 60 min
Marks: 42





Question No: 1 ( Marks: 1 ) - Please choose one
The Basic salary of an employee is Rs 7,000. What is the contribution of the company on account of gratuity to the Gratuity Trust Fund?

► Rs 636.36
► Rs 6363.6
► Rs 63.636
► Rs 6363

Question No: 2 ( Marks: 1 ) - Please choose one
The monthly incomes of A and B are in the ratio 4 : 5, their expenses are in the ratio 5 : 6. If 'A' saves Rs.25 per month and 'B' saves Rs.50 per month, what are their respective incomes?

►Rs.400 and Rs.500
►Rs.240 and Rs.300
►Rs.320 and Rs.400
►Rs.440 and Rs.550

Question No: 3 ( Marks: 1 ) - Please choose one
Sum of annuity is always

► Present value

► Future value

► Net present value

► Current value


Question No: 4 ( Marks: 1 ) - Please choose one
In annuity interest is charged by the:
► Simple interest method

► Compound interest method
► Both simple and compound interest method

► Accumulated method

Question No: 5 ( Marks: 1 ) - Please choose one
Find x if 3(x + 2) - 7 = 11.
► 2
► -4
► 6
► 4

Question No: 6 ( Marks: 1 ) - Please choose one
The value of x after solving the following linear equation is
-2x + 6 = 4x - 2

► 0
► 3
► 1/2
► 4/3

Question No: 7 ( Marks: 1 ) - Please choose one
The sequence of payments at equal interval of time is called
► Annuity

► Accumulated value

► Discounted value

► None of these


Question No: 8 ( Marks: 1 ) - Please choose one
Ali has improved his typing speed from 40w/m to 60w/m.The percentage improvement is

► 20%
► 150%
► 50%
► 30%

Question No: 9 ( Marks: 1 ) - Please choose one
Markdown means a reduction from the
► Original cost price

► Original sale price

► Original Net price

► None of these


Question No: 10 ( Marks: 1 ) - Please choose one

Markup is an amount added to ----------------------------------------

► get accumulated interest
► a cost price while calculating a selling price.
► The principal amount of the loan.
► Accumulation factor.

Question No: 11 ( Marks: 1 ) - Please choose one
Interest calculated upon the principal amount added to the interest on it is called ……

► Simple interest
► Compound interest
► Annual interest per year
► Semi annual interest

Question No: 12 ( Marks: 1 ) - Please choose one

Contribution Margin is the Rs. amount that is equal to ----------------------
► S – VC
► VC – S
► FC – VC
► VC – FC

Question No: 13 ( Marks: 1 ) - Please choose one
Reduction from original selling Price is called ………

► Loss
► List price
► Profit
► Markdown

Question No: 14 ( Marks: 1 ) - Please choose one
What will be the simple interest earned on an amount of Rs. 16,800 in 9 months at the rate of % p.a?

► Rs. 787.50
► Rs. 812.50
► Rs 860
► Rs. 887.50

Question No: 15 ( Marks: 1 ) - Please choose one
A percentage is a way of expressing a number as
►a fraction of 100 .
►sum of number with 100.

►multiplication of number with 100.

►average of number with 100.

Question No: 16 ( Marks: 1 ) - Please choose one
12.5% of a circular plot as a fraction is expressed as 1/8

►
►
►
►

Question No: 17 ( Marks: 1 ) - Please choose one
To convert a number in percent (%) from a fraction, we do which of the following operation:
►add by 100

►subtract by 100

►multiply by 100

►divide by 100


Question No: 18 ( Marks: 1 ) - Please choose one




What result will I get when press enter in cell D9?



►75
►B5+C5+D5+E5+F5
►Error
►Cannot be determine

Question No: 19 ( Marks: 1 ) - Please choose one
Interest paid (earned) on only the original principal borrowed (lent) is often referred to as
► simple interest
► present value
► future value
► compound interest

Question No: 20 ( Marks: 1 ) - Please choose one




By multiplying the above two matrices we get the following result
►
►
►
► Given matrices cannot be multiplied

Question No: 21 ( Marks: 1 ) - Please choose one
The formula for finding BEP in units is given by

► FC/VC
► FC/(S-VC)
► CM/FC
► CM/VC

Question No: 22 ( Marks: 1 ) - Please choose one
If A is a matrix whose determinant is zero then its inverse is given by:

► zero
► product of its diagonal entries
► infinite
► cannot be determined

Question No: 23 ( Marks: 1 ) - Please choose one
which of the following is linear equation

► 2x-3y=-6

► x+x+x

► 520x²y²

► y^2 -3=0


Question No: 24 ( Marks: 1 ) - Please choose one
percentage of ratio of given number with standard number is.......
►100
►Same number
►1000
►10

Question No: 25 ( Marks: 3 )
Find the single discount rate that is equivalent to the series18%, 12%, 9%.
Solution:

Let list price = 100

Series trade discount: Netprice = List price(1-d1)(1-d2)…..(1-dn)
= 100 (1 - .18)(1 - .12)(1 - .09)
= 100(.82)(.88)(.91)
=100(.657)
=65.7
Single discount rate = 100 – 65.7
= 34.3%



Question No: 26 ( Marks: 5 )
Compute the amount of compound interest for Rs 3500 at 6% per annum for 2 years.
Solution:

S = P(1+R/100)^n
S= Money accrued after n years also called compound amount
P= Principle amount
R= Rate of interest
n= number of periods

S= 3500 (1 + 6/100)^2
=3500 (1 + .06)^2
=3500(1.06)^2
= 3500(1.1236)
S=3933

Compound interest = S – P
= 3933 – 3500
= 433



Question No: 27 ( Marks: 10 )
It is advised by the exam department of an institute to the assistant to develop a structure of marks obtained by three students in three different subjects for very quick view & analysis with the following instructions to be followed strictly as;
a) marks obtained by EACH student in EVERY subject
b) marks in EACH subject be obtained by EVERY student.

Also describe & justify the optimality of the structure. If such model is possible then suggest its further extension for numerous numbers of students.

Solution: The optimal method to solve this problem is by using matrices

Let the student names be:
1. Ahmed
2. Shahzad
3. Amjad
Let the subjects be:
1. Math
2. Chemistry
3. Physics

Math Chemistry Physics
Ahmed 10 20 30
Shahzad 15 25 35
Amjad 20 25 45


Now let’s convert the above table into a matrix:

10 20 30
A = 15 25 35
20 25 45




BENEFITS OF MATRICES: The below benefits can help in further extension
1. Can handle large amount of data:
So w.r.t to the above question you can increase the no. of students & subjects as per your requirement and a
2. Analysis of data:
By using different matrix functions you can easily find out the respective averages and the grades of students.
3. Simple & Easy:
The above mentioned matix structure is simple and easy to understand and the data can be easily converted from table to matrix
4. Easy to evaluate performance:
Its easy to find each students performance in a specific subject
5. Easy extension:
As matrices can handle large amounts of data so you just need to enter the data rest is done by matrices functions.