Question 1
(A) Kojo and Alidu invested $4,000.00 and $6, 000.00 respectively in a business venture. After one year, a profit of $4,800.00 was realized. If after deduction of expenses of $1,280.00, the remainder is shared in proportion to their investment, find the amount received by each person.
(B) The 8th term of an Arithmetic Progression (A.P.) is -8 and the 3rd term is 12. Find the:
(i) common difference;
(ii) first term.
Observation
The Chief Examiner reported that a good number of candidates were able to tackle part(b) of this question. However, some candidates still had difficulty in understanding the requirement of the question. In part(a), majority of candidates that attempted it got the correct answer but some failed to indicate the decimal place in respect of the monetary answer.
In part(a), they did as expected by first finding the ratio as 2 : 3. Amount left after deduction
4800 – 1280.00 = $3,520.00. Kojo’s share is given as = $1,408.00 and Alidu’s share = = $2,112.00.
In part (b)(i), they did as expected by finding equation for 8th term a + 7d = – 8 ______(1) and equation for the 3rd term as a + 2d = 12 ______ (2). Solving gives common difference d as – 4.
In part (b) (ii), they did as expected by substituting – 4 for d in equation (1) or (2) to give first term, a = 20.