Theory question 110
Fractions, Decimals and Approximation(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 the family. 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 the: (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 installment at 25% per annum simple interest. If the Television set is purchased by installment, find the total cost.
Show the model answer
(a) Let the farm be x acres. Wife: 2/5 x; left 3/5 x; family: 1/3 × 3/5 x = 1/5 x
Children's part = x − 2/5 x − 1/5 x = 2/5 x
Least share = 2/10 × 2/5 x = 2/25 x = 8 ⇒ (i) x = 100 acres
(ii) Wife = 2/5 × 100 = 40 acres
(b) Balance = 1600 − 400 = $1,200; interest for 1 year at 25% = $300
Total cost = 400 + 1200 + 300 = $1,900
The least child's share is a fraction of the children's part, not of the whole farm.