Problem: A man loses 20% of his money. After spending 25% of the remaining, he has 510 left with him. How much money did he originally have?

Solution:

To solve this problem, we need to work backwards and use the given information to find the original amount of money the man had. Let's break down the solution into several steps:

Step 1: Calculate the amount of money remaining after losing 20%:
Let's assume the original amount of money the man had is 'x'.

20% of x can be calculated as (20/100) * x, which simplifies to 0.2x.
So, the amount remaining after losing 20% is x - 0.2x = 0.8x.

Step 2: Calculate the amount remaining after spending 25% of the remaining:
Now, the man spends 25% of the remaining amount, which can be calculated as (25/100) * 0.8x = 0.25 * 0.8x = 0.2x.
So, the amount remaining after spending 25% is 0.8x - 0.2x = 0.6x.

Step 3: Find the value of 0.6x:
According to the given information, the amount remaining after spending 25% is 510.
So, we can set up an equation:
0.6x = 510.

Step 4: Solve the equation to find the value of x:
Dividing both sides of the equation by 0.6, we get:
x = 510 / 0.6 = 850.

Step 5: Interpret the result:
Therefore, the man originally had 850 units of money.

Summary:
- The man originally had 850 units of money.
- He lost 20% of his money, leaving him with 0.8x.
- After spending 25% of the remaining, he had 0.6x left.
- The amount remaining after spending 25% was given as 510 units.
- By solving the equation 0.6x = 510, we found that x = 850.