(a) In a man’s will, he gave \(\frac{2}{5}\) of the total acres of the farm to the wife and \(\frac{1}{3}\) 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 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 installments at 25% per annum simple interest. If the Television set is purchased by installment, find the total cost.
Explanation
let the total Acres = x
Wife's Share = \(\frac{2}{5} \times x = \frac{2x}{5}\)
Remaining part = x - \(\frac{2x}{5}\) = \(\frac{3x}{5}\)
Part for family = \(\frac{1}{3}\) x \(\frac{3x}{5}\) = \(\frac{x}{5}\)
Remaining part = x - (\(\frac{2x}{5}\) + \(\frac{x}{5}\)) = \(\frac{2x}{5}\)
Total ratio = 2 + 5 + 2 = 10
Child with least share = \(\frac{2}{10}\) x \(\frac{2x}{5}\) = 8
x = \(\frac{8 \times 25}{2}\) = 100 acres.
(ii) Acres wife received = \(\frac{2}{5}\) x 100 = 40 acres.
(b) If $400 is deposited, the remaining amount to be paid will be = $1600 - $400 = $1200.
so, P = $1200, T = 12months = 1 year, R = 25%
Therefore, S.I = \(\frac{1200 \times 25 \times 1}{100}\) = $300
But, Total cost = initial deposit + principal + interest = $400 + $1,200 + $300 = $1,900