QUANTITATIVE METHODS (MARKS 100)
Module A (3 hours)
Q.1 (a) If log xy = 0.9 and log x/y = 0.5, find the following, without using a
calculator/table:
(i) log 2
x
(ii)
log y (03)
(b) Factorize the following expression to its simplest form:
2222 bybxayax −+− (02)
Q.2 (a) Ali walked a certain distance on the first of February 2009. On each successive day
he walked 100 meters more than the previous day. If the total distance covered by
him in 28 days is 51.8 km, find the distance covered by him on:
(i) the first day
(ii) the last day (04)
(b) Asif works in a factory where wages are paid on weekly basis. The overtime rate is
higher than the normal rate. In addition, the overtime in excess of eight hours per
week is paid at a rate which is double the rate applicable to the first eight hours of
overtime. The related data is as follows:
Normal Hours Overtime Hours Pay Received (Rs.)
1st week of Feb’ 09 45 10 1,200
2nd week of Feb’ 09 40 15 1,350
Find the normal and overtime rates per hour. (05)
Q.3 (a) A company is considering a project which requires an investment of Rs. 1,200,000
now and Rs. 300,000 at the end of the 1st year. It will earn Rs. 200,000 at the end of
2nd year and thereafter it will earn a fixed annual amount up to the 7th year.
If interest rate is 11%, find the amount that the project should earn annually i.e.
from year 3 to year 7 if the company desires to earn a net present value of
Rs. 100,000. (07)
(b) Younus Limited (YL) has borrowed an amount of Rs. 100,000 at an interest of
10% per annum compounded semi-annually. To pay off the loan at the end of four
years, YL has created a sinking fund, which yields a return of 8% per annum
compounded quarterly. Determine the amount which YL must deposit at the end of
each quarter, in the sinking fund, to settle the loan at the end of four years? (05)
Q.4 (a) If y = xexlog x, show that:
()
xey
dx
dy xlog1++= (05)
docsity.com
