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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)
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