# CWA ICWA Foundation : Business Mathematics and Statistics Fundamentals - December 2003

 C—4(BMS)Revised Syllabus Time Allowed : 3 Hours Full Marks : 100
 The figures in the margin on the right side indicate full marks. Section A ARITHMETIC (15 marks)Answer Question No. 1 (compulsory – 5 marks) and any one(10 marks) from the rest. Marks
 1. (a) The ratio of the present age of a father to that of his son is 5 : 3. Ten years hence the ratio would be 3 : 2. Find their present ages. 2 (0) (b) After spending 69% of his money a person has Rs.93 left. How much had he at first? 2 (0) (c) Calculate the interest on Rs.10,000 for 10 years at 10% p.a. 1 (0) 2. (a) X, Y, Z are three children. Y was born when X was 4 years 7 months old and Z was born when Y was 3 years 4 months old. Find the average age when Z was 5 years 2 months old. 5 (0) (b) A radio–dealer offers a radio for Rs.270 cash down or Rs.30 cash down and 18 equal monthly installments of Rs. 15 each. Find the rate of simple interest charged. 5 (0) 3. (a) The true discount (TD) on a bill for Rs.2,160 due sometime hence is Rs.180; find the Banker’s gain (BG) on the same bill at the same rate. 5 (0) (b) A dealer mixes tea costing Rs.8 per kg with tea costing Rs.7 per kg and thereafter, sells the mixture at Rs.8 per kg and earns a profit of 7.5% on his sale price. In what proportion does he mix them? 5 (0)
 Section B ALGEBRA (25 marks) Answer Question No.4 (compulsory – 5 marks) and any two (10 x 2 = 20 marks) from the rest.
 4. (a) Write 1.35 as a rational number. 1 (0) (b) Find the logarithm of 0.0001 to the base 0.1 2 (0) (c) Exhibit the following set in tabular form A = {x : x ∈N, x < 8 is odd}, where N is the set of natural numbers. 2 (0) 5. (a) Find the square root of 7 + 24i. 5 (0) (b) If one root of ax2 + bx + c = 0 is four times the other, then show that 4b2 = 25 ca. 5 (0) 6. (a) If p = log10 20 and q = log10 25, find x such that 2 log10(x + 1) = 2p − q. 5 (0) (b) In how many ways can the letters of the word MONDAY be arranged? How many of them do not begin with ‘M’? How many of them do not begin with ‘M’ and end with ‘Y’? 5 (0) 7. (a) The total expenses of a hostel are partly constant and partly vary as the number of boarders. If the expenses for 120 boarders be Rs.20,000 and for 100 boarders be Rs.17,000, find for how many boarders will cost come to Rs.18,800? 5 (0) (b) Prove with the help of a Truth table that (~p ∨ q) ∧ (~q ∨ p) = p ⇔ q. 5 (0)
 Section C MENSURATION (30 marks) Answer Question No.8 (compulsory – 6 marks) and any two (12 x 2 = 24 marks) from the rest.
8.(a)2 (0)
(b)2 (0)
(c)2 (0)
9.(a)6 (0)
(b)6 (0)
10.(a)6 (0)
(b)6 (0)
11.(a)6 (0)
(b)6 (0)
 Section D ELEMENTARY STATISTICS (30 marks) Answer Question No. 12 (compulsory – 6 marks) and any two (12 x 2 = 24 marks) from the rest.
12.(a)1 (0)
(b)2 (0)
(c)3 (0)
13.(a)6 (0)
(b)6 (0)
14.(a)4 (0)
(b)8 (0)
15.(a)6 (0)
(b)6 (0)  