| ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS) | ||
| END SEMESTER EXAMINATION – SEPT/OCT. 2015 | ||
| B.Com (Regular)– I Semester | ||
| C1 15AR104: MATHEMATICS FOR MANAGERS | ||
| Duration: 3 Hours Max. Marks: 100 | ||
| SECTION – A | ||
| I) | Answer ALL the questions. Each carries 2 marks. (10×2=20) | |
| 1. | Moti is a very dishonest trader. He cheats his customer using false weights. Therefore, instead of using a 1 Kg weight, he uses an 800 gm weight. What is his gain % from this unethical activity? | |
| 2. | A number decreased by 33.5% gives 532. Find the number. | |
| 3. | A regiment of 700 men has rations that will last them 33 days. However a new contingent of 70 men joined them. Now, how long will the rations last for? | |
| 4. | If Selling Price = Rs.880, Cost Price = Rs.800 and List Price = Rs.1100, Calculate percentage of profit/loss and percentage of discount. | |
| 5. | Mr. Ahemed wants to institute a prize for mathematics in memory of his brother. If the annual cash prize is to be Rs.5000 and the rate of interest is 8%, what amount should he deposit today? | |
| 6. | Differentiate y = 1/x-1/2 + e(2x+3) | |
| 7. | Solve using simultaneous equation method:
6x-5y=10 3x+2y=23 |
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| 8. | The weekly wages of 30 people comprising of men and women amount to Rs. 190. If each man receives Rs. 7 and each woman Rs.5, find out the number of men and women. | |
| 9. | In how many years will a sum of money double itself if compound interest is applied at 8% p.a.? Verify your answer with Rule of 72. | |
| 10. | If USD/INR = 66.24, convert Rs.1,50,000 into dollars. | |
| SECTION – B | ||
| II) | Answer any FOUR questions. Each carries 5 marks. (4×5=20) | |
| 11. | Innovators Inc. has won a contract for the supply of their newly designed hover board. The prototype constructed to win the contract took 500 hours. It is expected that there will be 90% learning effect. Estimate the labour cost of producing 7 more hover boards of new order if the cost of labour is Rs.60 per hour. | |
| 12. | Differentiate:
a) Y = (2x2 + 3x + 2) / ex b) Y = x3logx + 3x-1/3
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| 13. | A firm borrows Rs. 30, 000 from a bank at 10% p.a. This loan has to be repaid in 5 years. Find the loan installment and draw the amortization schedule. | |
| 14. | Find the present value of inflows of Rs.1000, Rs.1500, Rs.2000, Rs.2200 and Rs.3000 receivable in the 1st, 2nd, 3rd, 4th and 5th year respectively. Discount rate 10%
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| 15. | A bill for Rs. 14,600 drawn at 3 months after date was discounted on 11th November, 2000 for Rs. 14, 320. If the discount rate is 20% p.a… On what date was the bill drawn? | |
| 16. | Beginning on his 41st birthday and ending on his 65th Birthday, Ram deposited a sum of Rs. 500 per year in a fund which paid him effective rate of interest at 3% p.a . What amount is due to him on his 65th Birthday? | |
| SECTION – C | ||
| III) | Answer any THREE questions. Each carries 15 marks. (3×15=45) | |
| 17. | a) Mr. Prakash decides to purchase a machine for Rs. 2,00,000. He agrees to pay for the machine in 5 equal annual installments at the end of each year. The effective rate is 5%. What is the size of each installment?
In case Mr. Prakash makes a down payment of Rs. 50000, then what would be the size of each installment?
b) What is the difference between the Compound Interest and Simple interest of a sum of Rs. 4000 invested at a rate of interest 15% for a period of 5 years? (10+5) |
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| 18. | a) i) An initial trial batch of 40 solar panels takes Green Energy Ltd a total of 5000 labour hours. They have now received a contract for 120 panels. Learning effect is expected at 80%. Estimate labour costs per panel if the cost per hour is Rs. 45.
ii) In addition to labour cost, the material cost is Rs. 2000 per panel and variable overhead is Rs. 500 per unit. What should be the price of each panel to ensure a profit of 15%
b) Find the present value of a sequence of payments of Rs.125 made at the end of each quarter and continuing for ever, if the effective rate of interest is 8%. What if payments are made half yearly? (10+5) |
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| 19. | a) Evaluate the following business decision and decide which project to choose
Project A Initial investment Rs.1,00,000 Annual Cash inflows: Rs.30,000 Project B Initial investment Rs.80,000 Annual Cash inflows: Rs.20000 Both projects span 5 years and the discount rate is 8%pa
b) A sum of Rs.1000 is compounded quarterly at 16% p.a for a period of 3 years. Find the amount and the effective rate of interest. (10+5) |
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| 20. | A bill for Rs. 1712.75 was drawn on 3/4/15 and made payable 3 months after date. It was discounted on 15/4/15 at 16.5%p.a.
i) What is the discounted value of the bill ii) How much has the banker gained on this transaction?
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| 21. | a) The total cost C of output Q is given by the following C = 300Q – 10Q2 + Q3/3. Find the output levels at which the Average Cost and Marginal Cost attain their respective minimums. Also find the minimum AC and MC.
b) A machine costing Rs.80,000 depreciates in value 5% during the first year, 7% during 2nd year and 10% during next 6 years. Find the value of the machine at the end of 8 years. (10+5) |
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SECTION – D |
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| IV) | Case Study (1×15=15) | |
| 22. | a) The cost function C = 5 + 4Q + 0.6Q2 and the Demand Function P = 12 – 0.4Q, where Q is quantity and P is price. Calculate the following
i) Total Cost when 100 units are produced ii) Average cost when 25 units are produced iii) Marginal Cost when 50 units are produced iv) Level of output at which profit is maximized v) If 200 units are produced at what price should each unit sell at so as to achieve break even?
b) Find the maximum and minimum values of the following function- y= 3x3– 9x2-27x+30
(10+5) |
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