A man had a certain amount with him. He spent 25% of that to buy an article and 10% of the remaining on clothes. Then he donated Rs 531.25. If he is left with Rs. 8000 the amount he spent on the clothes is

Answer

To solve the problem step by step, let's denote the initial amount of money the man had as \( x \).

### Step 1: Calculate the amount spent on the article
The man spent 25% of his total amount \( x \) to buy an article.
\[ \text{Amount spent on article} = 0.25x \]

### Step 2: Calculate the remaining amount after buying the article
After buying the article, the remaining amount is:
\[ \text{Remaining amount} = x - 0.25x = 0.75x \]

### Step 3: Calculate the amount spent on clothes
The man then spent 10% of the remaining amount on clothes.
\[ \text{Amount spent on clothes} = 0.10 \times 0.75x = 0.075x \]

### Step 4: Calculate the amount left after spending on clothes and donating
After spending on clothes, the amount left before donation is:
\[ \text{Amount left before donation} = 0.75x - 0.075x = 0.675x \]
He then donated Rs 531.25, so the amount left after donation is:
\[ \text{Amount left after donation} = 0.675x - 531.25 \]

### Step 5: Set up the equation with the amount left
According to the problem, he is left with Rs 8000 after the donation:
\[ 0.675x - 531.25 = 8000 \]

### Step 6: Solve for \( x \)
Now, we can solve the equation for \( x \):
\[ 0.675x = 8000 + 531.25 \]
\[ 0.675x = 8531.25 \]
\[ x = \frac{8531.25}{0.675} \approx 12640.74 \]

### Step 7: Calculate the amount spent on clothes
Now that we have \( x \), we can find the amount spent on clothes:
\[ \text{Amount spent on clothes} = 0.075x = 0.075 \times 12640.74 \approx 948.06 \]

Thus, the amount spent on clothes is approximately Rs 948.06.