Quantitative Techniques

 

ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)
END SEMESTER EXAMINATION – SEPT/OCT. 2015
b.b.a.(International Students) – I semester
QUANTITATIVE TECHNIQUES
Duration: 1 1/2  hour                                                                                          Max. Marks: 50
SECTION – A
I)	Answer any 6 of the following questions.  Each carries 2 marks.                (2×6=12)
	1.	In a wrestling competition the total weight of the two contestants is 700 pounds. If twice the weight of the first contestant is 275 pounds more than the weight of the second contestant, what is the weight (in pounds)of the first contestant?. Use Analytical Geometry method.
	2.	Suppose a manufacturer finds that the cost y of producing x units of a certain commodity is given by the formula y=2x+5000, what  interpretation can be given to the slope of the graph of this equation?
	3.	If the third term and the 6th term of an A.P are 7 and 13 respectively, find the first term and the common difference.
	4.	Insert 5 geometric terms between 9 and 576.
	5.	Angel wants to buy a Jet plane which is worth Rs.23,00,000. She embarks on a saving scheme in an AP in which she first saves Rs.150,000 and increased her subsequent saving by Rs.2,000 each month. Determine how much she will need to borrow in order to achieve her dream by the time  she has saved 8 times on a monthly basis
	6.	Mr. Teghen wants to embark in a saving scheme. He decides that the minimum amount he should save in any one year should be Rs.100,000.  At the end of the first year, he saves Rs.100,000 and save an additional Rs.5000 each succeeding year. How much shall he have saved by the end of the 30th year?
	7.	An investor deposits $15000 in a bank account. The bank offers an interest rate of 4.1 % per year. a)        What is the value of the investment 4 years later? b)       How much time is needed for the amount to double?
	8.	A person wishes to buy a motorcycle worth $12000. In Order to collect this amount, he deposits an amount V at the bank, and lets it flourish for 5 years at an interest Rate of 5 %, capitalized biannually. Find V.
SECTION – B
II)	Answer any Three questions.  Each carries 6 marks.                                    (3×6=18)
	7.	The value V of an asset t years after purchase is V= – 100,000t + 7,00,000. The expected life of the asset is 5 years. How much did the asset originally cost? What is the annual deduction for depreciation? What is the salvage value of the assets?
	12.	Three numbers whose sum is 15 are in AP. If 1, 4 and 19 are added to them respectively, the results are in GP. Find the three numbers.
	13	A toy manufacturer is currently producing 2000 toys a week beginning in October; the manufacturer will begin to increase production each week by 500 more toys during each week of the Christmas production season. The relationship between the week w and the nos of toys produced P is linear. a) Find the equation that describes this relationship b) interpret the slope of the linear relationship c) Find P when w=5, Interpret the solution in terms of toy production.
	14	The supply curve of a certain commodity is the straight line p=.002q+2(p in Rs.) and the demand curve for the same is p= -0.0005q+5.5. Determine both the quantity of the commodity that will be produced and the price at which it will sell on stabilization.
SECTION – C
III		Compulsory questions.                                                            (2×10=20)
	15.	The demand function of a radio is Qd=3000-5p, when Qd is the quantity demanded per year and ‘P’ is the price per set of radio.. a) Construct a demand schedule and plot it on a graph at prices 150,250 and 325,400 and 500(all in Rs.) b) Also find out at what price Qd=0? c) And if the seller wants to sell 2500 sets what price should be fixed by the radio company?
	16.	The following table shows the hypothetical monthly demand and supply schedules for cans of macadamia nuts in Hawaii.   Price ($) Qty demanded(in cans) Quantity supplied(cans)   6 700 100 7 600 200 8 500 300 9 400 400 10 300 500 a. Plot this on the graph sheet to find out what is the equilibrium price of macadamia nuts in Hawaii     b. At a price of $7 per can, is there equilibrium, a surplus or a shortage. If it is a surplus or shortage, how large is it?   c. At a price of $10, how large is the shortage or surplus?

 

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3. if the 3^rd term and the 6^th terms of an ap is 7 and 11 find the first term and the cd.

 

First term 3 and the CD is 2.(MARKS 1+1)

4. Insert 5 geometric terms between 9 and 576

The terms are 18,36,72,144,288(MARKS 1 FOR WORKING, 1 FOR ANS)

5. Sri. S.Roy borrows rs.32,760 without interest and agrees to pay back in 12 monthly installments, each installments being twice the preceding one. Find the second and the last installments.

2^nd install- Rs.16 and the last installment- 16384.

12.Three numbers whose sum is 15 are in AP. If 1, 4 and 19 are added to them respectively, the results are in GP. Find the three numbers.

a-d, a and a+d are the number in AP

a-d+a+a+d=15

so a=15

a-d+1,a+4 and a+d+19 are in GP

substituting a=15 in the above, d=3 or -21

• When d=3, the number are 2,5,28
• When d=-21, the numbers are 26,5,-16.