Question

10. (a) In a man's will, he gave 2/5 of the total acres of his cocoa farm to the wife and 1/3 of what is left to be shared for family upkeep. The rest of the farm was to be shared amongst his three children in the ratio 3:5:2. Given that the child who had the least share received 8 acres, calculate: (i) total acres the man left; (ii) number of acres the wife received.
(b) The list price of a television set is $1,600.00. It can be purchased by a deposit of $400.00 and the rest of the amount paid by 12 monthly instalment at 25% per annum simple interest. If the television set is purchased by instalment, find the total cost.

Accepted Answer

(a) Let total acres = T. Wife's share = 2/5T. Remainder = 3/5T. Of this remainder, 1/3 goes to family upkeep, leaving 2/3 × 3/5T = 2/5T for the three children, shared in ratio 3:5:2 (total 10 parts).
Least share (2 parts) = 8 acres → 1 part = 4 acres → children's total share (10 parts) = 40 acres = 2/5T.
(i) T = 40 × 5/2 = 100 acres.
(ii) Wife's share = 2/5 × 100 = 40 acres.

(b) Deposit = $400. Balance = $1600−$400 = $1200, paid over 12 months (1 year) at 25% p.a simple interest.
Interest = PRT/100 = (1200×25×1)/100 = $300.
Total instalment payments = $1200+$300 = $1500.
Total cost = Deposit + Instalment total = $400+$1500 = $1900.

NECO Mathematics 2024 Theory — Question 10

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