A fruiterer bought some longans. 2/5 kg of the longans were rotten and he threw them away. Then he sold 1/5 Of the remaining longans and had 16 kg of longans left. How many kilograms of longans did the fruit seller buy?
Let X be the number of kg of longans bought.
The number of rotten longans is X * 2/5 = X/5.
Thus, the number of longans left is X - X/5 = 4X/5.
The number of longans sold is 4X/5 * 1/5 = 4X/25.
So the number of longans left is 4X/5 - 4X/25 = 16 kg.
Thus, 4X/25 = 16
Thus, X = 16 * 25/4 = <<16*25/4=100>>100 kg. Answer: \boxed{100}.
Let's break down the information given step-by-step to find the answer:
Step 1: The fruiterer initially had a certain amount of longans.
Let's say the initial weight of the longans is x kg.
Step 2: 2/5 kg of the longans were rotten and discarded.
The remaining weight of the longans after discarding the rotten ones is x - (2/5) kg.
Step 3: The fruiterer sold 1/5 of the remaining longans.
The amount of longans sold is (1/5) * (x - 2/5) kg.
Step 4: After selling, the fruiterer had 16 kg of longans left.
So, the equation becomes:
(x - 2/5) - (1/5) * (x - 2/5) = 16.
Simplifying the equation:
5(x - 2/5) - (x - 2/5) = 80,
5x - 2 - x + 2/5 = 80,
4x - 2/5 = 80,
4x = 80 + 2/5,
4x = 400/5 + 2/5,
4x = 402/5,
x = (402/5) * (1/4),
x = 402/20,
x = 20.1.
Therefore, the fruiterer initially bought 20.1 kg of longans.