Mathematics For Managers

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ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)
END SEMESTER EXAMINATIONS – OCTOBER 2013
BCOM – I SEMESTER
MATHEMATICS FOR MANAGERS
Time: 3 Hrs Max Marks: 100
SECTION – A
I) Answer ALL questions. Each carries 2 marks. (10 x 2 = 20)
1. Find the number of years in which an investment of Rs.16,000 at 12% simple
interest will amount to Rs.21,760.
2. Ratio of investments of A, B and C is given by A:B = 3:4 and B:C= 8:9. Find the
share of C out of total profit of Rs.23,000.
3. An item is listed at Rs. 150 with a discount of 20%. What additional discount must
be offered to the customer to bring the net price to Rs. 108?
4. Find the amount and compound Interest on Rs.10,000 for 3 years at 8% per annum,
interest being payable quarterly.
5. A machine depreciates at the rate of 7% of its value at the beginning of the year. If
the machine was purchased for Rs.18,500 and its lifetime is 6 years, find the scrap
value of the machine.
6. A company manufactures specialized equipment. The average labour hours taken
to manufacture the first 8 equipments is 1024 Hrs. A repeat order to manufacture 8
more equipments is received. If the learning effect is 80% find the time taken to
manufacture the new order.
7. If true discount on a certain sum of money is Rs.300 and banker’s discount is Rs.3
more. Find the face value of the bill.
8. Solve for x, 14 – 5(x-4)(x+8) = 188 – 5(x+3)2
9. Differentiate Y= 2×4 + 3×5 – 4×2/3+ 5x + 6
10. If the total cost function C of a firm is given by C= 200 + 6×2-2x. Identify the fixed
cost. What is the cost of manufacturing 50 units?
SECTION – B
II) Answer any FOUR questions. Each carries 5 marks (4 x 5 = 20)
11. Find minima point of the function y= 27 – 6x + x2. Also find the minimum value of
the function
12. A person purchased a vehicle and agreed to pay Rs.15,000 down payment and a
monthly installment of Rs.3000 for 2 years. If the rate of interest is 12% per annum
what is the present value of the vehicle.
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13. A sum of money invested at CI amounts to Rs.10,816 at the end of 2nd year and
Rs.11,248 at the end of 3rd year. Find the rate of interest and the sum invested.
14. A company sells a single product for Rs.65 per unit. Variable costs per unit are Rs.
20 for materials and Rs.27.50 for labour. Annual fixed costs are Rs.1,00,000.
Construct the Revenue function, Cost function and the Profit function. What profit
is earned if annual sales are 20,000 units.
15. A contractor estimates that, for certain building materials and wages will cost him
Rs.16,000 and 12,000 resp. To the total he adds 15% as profit and quotes the
amount for the job. But when the work is undertaken, materials have decreased in
cost by 5% while the wages have risen by 10%. Find his actual profit percent
correct to two decimal places.
16. You are planning a trip to USA and Europe, for which you buy 1000 USD and 2000
Euros. The current rate for for USD is Rs.62 USD/INR and the current rate for EUR
is Rs.84 EUR/INR.
Your trip gets cancelled and exchange rates have changed. The new rates are
USD/INR 64 and EUR/INR 82. How much do you gain or lose due to cancellation
of the trip and conversion back to Indian Rupees?
SECTION – C
III) Answer any THREE questions. Each carries 15 marks (3x 15 = 45)
17. a) A company borrows Rs.5,00,000 at an interest rate of 14%. Loan is to be repaid in
4 equal annual installments payable at the end of each of the next 4 years. Find the
installment amount and prepare the loan amortization schedule.
b) A man deposited Rs.5000 in a Savings Bank which pays compound interest at
the rate of 6.5%p.a. for the first two years and then at the rate of 7% for the next
three years. Find his amount after 5 years. What was the interest received? If the
same sum Rs.5,000 was deposited at 7% simple interest for the entire 5 years.
What is the difference in interest received?
( 8 + 7)
18. A bill for Rs 27,000 was drawn on 23rd September ,2011 at 6 months date and
discounted on 13th November ,2011 at the rate of 8.5% p.a. For what sum was the
bill discounted? How much did the banker gain in this transaction?
19. A Company has been approached by a customer to supply 64 units of a new
product made to the customer’s individual specification. The company experiences
a 90% learning rate. The estimated labour time for the first unit of this product is
122 Hrs. direct labour cost is Rs. 4 per hour. Material cost is Rs.3500 per unit. Fixed
overheads is Rs.10,000.
a) Using the learning curve concept estimate the average cost of making 64 units.
b) If 128 units were manufactured what difference does it make to the average cost.
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20. a) Differentiate using product rule Y = (2×2-3x+4)(x3+3)
b) Differentiate using quotient rule Y = 8X5+ 4X3
4X2 – 13X
c) Find Yl and Yll Y= logx +5xex – 7×7 ( 5+5+5)
21. a) Find the expression for the elasticity of demand for the demand function
x=250- p-0.05p2, where p is price in Rs. and x is quantity. Evaluate the expression
where price is Rs. 10 and interpret your result.
b) An engineering company has succeeded in winning an army contract work
for supplying engines of a new type. The trial order of 5 engines took 750 hrs
of labour. The army has given a new contract for 45 more engines. Find the
labour time taken for the new order. Learning effect is 80%.
c) You have a choice between Rs.5000 now and 20,000 after 10 years. Which
would you choose? What does your preference indicate? Interest rate is
10%. (5+5+5)
SECTION – D
IV) Compulsory Question (1 x 15 = 15)
22. a) Hidesign has examined its cost and revenue structure and has determined that
total cost C, the total revenue R and the number of units produced x are related
as C= 680 + 15x – 0.5×2 and R= 350x- 3×2 . Find a) Fixed cost b) Average
cost c) Marginal cost d) Price e) Marginal revenue f) Profit maximizing output.
b) A machine costs a company Rs.2,38,000 after 5 years. How much money out of
profits should be set aside every year to realize the sum at 12% per annum
compound interest. If savings can be done quarterly what should be the amount
saved? (7+8)

 

 

1. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

END SEMESTER EXAMINATION – OCTOBER 2014

1. COM – I SEMESTER

 MATHEMATICS FOR MANAGERS

Duration: 3 Hours                                                                                       Max. Marks: 100

SECTION – A

 

1. Answer ALL the questions. Each carries 2 marks.                                       (10 x2 =20)

 

1. Solve 8x²-10x+3=0 using formula method.
2. In the two consecutive numbers, 1/4^th of the smaller one exceeds the 1/5^th of the larger one by 3. Find the numbers.
3. Adarsh bought goods worth Rs. 20, 000. He was offered trade discount of 25% and further received a cash discount of 10%. Find the net price that he had to pay.
4. Out of 60 students, 20 passed. Find the percentage of failure.
5. What is Inverse proportion?
6. If 3/5^th of an estate is worth Rs.1, 800. Find the value of 2/3^rd of it.
7. y=1/x and y=(1/x⁴ )- e^x + x. Then find dy/dx
8. If f(x) = 2x+3. Find f(-3)+f(1)
9. If the Total cost function is C= 2x²+x+10 and the quantity produced is 10 units. Find the variable cost and the fixed cost.
10. The total cost of an article was Rs.24 and its selling price was marked at S. Later it was offered for sale at 90% of this selling price. The dealer still made a profit of 10% of his original cost. What was the marked price?
11. An Indian merchant imports goods worth Rs.24, 990 pounds. If the exchange rate is GBP/INR: 100. How much is it worth in Indian rupees?

 

                                                SECTION – B

 

1. Answer any FOUR Each carries 5 marks.                                  (4×5=20)
2. a. Divide 5, 000 in the ratio given- A:B is 2:3 and B: C is 4:3
3. 5 men each working 9 hours a day can finish a work in 30 days. How many men are required to finish 8 times the work in 25 days each working eight hours a day.

 

12. a. The population of a village 2 years ago was 6250. Due to migration to cities for higher education etc.., it decreases every year at 4% p.a. Find the present population of the village.
13. A machine depreciates in value each year at 10% of its value at the beginning of a year. If the machine is purchased at Rs.15, 000, find its value at the end of the 3^rd year.
14. If the banker’s gain on a bill is 1/9^th of the banker’s discount. The rate of interest being 10% p.a. Find the unexpired period of the bill.
15. Differentiate the following:
16. y= 2e^x + 2^x + 2/x + 7 logx
17. y= (2x² – x) (3x² + x-1)

 

15. Define Learning curve. It is highly impractical to achieve a learning effect of 50%. Illustrate with learning curve table.
16. a. Parents of Krishna want to send him to London after 7 years. He expects the cost of the trip will be Rs.5, 00, 000. How much should he save semi annually to have Rs. 5, 00, 000 after seven years, if the interest rate is 12% p.a.
17. Bank of Baroda offers 12% p.a. interest on 12 months recurring deposit account. If I deposit Rs.1, 000 per month for 12 months, how much can I get at the end of 1 year assuming that each deposit is to be made at the beginning of the month?

 

SECTION – C

 

III)      Answer any THREE questions.    Each carries 15 marks.                    (3×15=45)

 

17. a. Karan buys a two wheeler on loan. The loan amount is Rs.60, 000. He wants to clear the loan in 10 months. How much should he pay every month? Prepare the loan amortization schedule. Interest charged is 18 % p.a.
18. A man invests Rs.5, 000 for 3 years at a certain rate of interest compounded annually. At the end of one year it amounts to Rs.5, 700.
19. Calculate the rate of interest per annum.
20. The interest accrued in the second year.

iii. The amount at the end of the third year.

(10 +5)

18. a. The manufacturer’s total cost function is C= 500+25x+x². Find the variable cost when 10 units are produced,  Average cost function, Marginal cost function, Marginal cost when 10 units are produced, and Actual cost of producing 11^th unit.
19. x= 32-4p-p², when p=3. Find the elasticity of demand.

(10 + 5)

19. a. If you deposit Rs.5, 000 today at 12% p.a. C.I. In how many years will the amount grow to Rs.1, 60, 000?
20. Which is better Rs. 55, 000 now or Rs. 90, 000 after 3 years at 15% p.a. C.I.
21. A loan of Rs. 1, 00, 000 is taken on which interest is payable at 10% p.a. C.I. However, the repayment is to start at the end of 3^rd year from now. What should be the annual payment if the total loan and interest is to be repaid in 9 installments?

(5+5+5)

20. a. A bill of Rs. 1, 700 was drawn on 3^rd April 2000 and made payable 4 months after date. It was discounted on 15^th April 2000 at 16 % p.a. What was the discounted value of the bill and how much has the banker gained on this transaction.
21. A bill for Rs.2, 920 was drawn on September 11^th for 3 months after date and was discounted at 16% p.a. for Rs. 2, 875. On what date was the bill discounted?

 

21. a) Find the simple interest compound interest and their difference on Rs.5000 invested for 4 years at 8% Per Annum.
22. b) An Investment, which requires an initial outlay of Rs.100000, Will yield an annuity of Rs.20000 for 12 years. If the discount rate is 14% per annum should we accept this investment proposal?
23. c) Steve has an option of investing Rs. 1200 at 8% P.a for 2 years with the following alternatives
24. Interest calculated annually.
25. Interest calculated half yearly.

• Interest calculated quarterly.

1. Interest calculated monthly.

Which of the 4 above alternatives would you recommend Steve and why?

(5+5+5)

SECTION – D

1. IV) Compulsory question. (15 marks)
2. a. i)A company has been asked to bid for prospective contract for the supply of 90 engines. They have just completed an initial trial order for 30 engines involving a total of 6, 000 direct labour hours at Rs. 50/ hour. It is expected that there will be an 80% learning effect. Estimate labour cost for the new order.

ii). If material cost if Rs.5, 000 per engine, variable overheads is Rs.12 per direct labour hour, fixed overhead is Rs.5, 600. Profit expected is 12.5% over cost. Find the price per unit that can be quoted for the contract.

 

1. b) Find Maximum profit if R= 30X-X² and C=20+4X

(10+5)