QUANTITATIVE METHODS (MARKS 100)
Module A (3 hours)
Q.1 (a) Find the values of x and y in the given set of simultaneous equations:
5
4
1
1=
+
+
y
x and 2
1
5
5=
−
−
y
x (05)
(b) Find the equation of a straight line which intersects the y-axis at y = 4 and
the x–axis at x = 8. (04)
Q.2 (a) Using log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of:
(i) Log 4.5
(ii) Log 52 (04)
(b)
If x
exy 2
2ln += show that xy
xe
dx
dy x
2
21 2
+
= (04)
Q.3 (a) How much should an individual deposit now to yield Rs. 600,000 at the
end of five years in each of the following situations:
(i) At 10% simple interest
(ii) At 9% compounded half yearly (05)
(b) Ashraf purchased a new car and made a down payment of Rs. 50,000. He
is further required to pay Rs. 30,000 at the end of each quarter for five
years. You are required to:
(i) Find the cash purchase price of the car, if the quarterly payments
include 12% interest per annum compounded quarterly.
(ii) Find the total amount of interest Ashraf has to pay. (05)
Q.4 (a) The revenue function for a product is:
2
2400 qqTR −=
The average cost function is:
q
qAC 400
42.0 ++= , where q is the number of units
Determine the following:
(i) Level of output at which profit is maximized.
(ii) Price at which maximum profit occurs.
(iii) Amount of maximum profit. (07)
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