A man made a will in which he left 4/9 of his money to his wife and 2/5 of the remainder to his eldest child. The rest was to be shared equally among his four younger children. If each of the younger children received ₦54,000, what was the wife's share?
Let X be the total amount of money the man had.
The wife received 4/9*X.
The remainder is X - 4/9*X = 5/9*X.
The eldest child received 2/5 * (5/9*X) = 2/9*X.
The four younger children received a total of 4 * ₦54,000 = ₦<<4*54000=216000>>216,000.
Each younger child received ₦216,000 / 4 = ₦<<216000/4=54000>>54,000.
The total amount of money was 4 * ₦54,000 = ₦<<4*54000=216000>>216,000.
So, X - (4/9*X + 2/9*X) = ₦216,000.
This simplifies to 3/9*X = ₦216,000.
Thus, X = (₦216,000) * (9/3) = ₦<<216000*(9/3)=648000>>648,000.
Therefore, the wife's share was 4/9*X = (4/9) * ₦648,000 = ₦288,000. Answer: \boxed{288,000}.