Samu spent `1/4` of his money on books and 1/8 on food. If if left with 40, how much did he spend on food?

Options

A. 12
B. 8
C. 6
D. 10

Answer

To solve the problem step by step, we will first define the total amount of money Samu had and then calculate how much he spent on books and food.

### Step 1: Define the total amount of money
Let the total amount of money Samu had be \( X \).

### Step 2: Calculate the amount spent on books
Samu spent \( \frac{1}{4} \) of his money on books. Therefore, the amount spent on books is:
\[ \text{Amount spent on books} = \frac{1}{4}X \]

### Step 3: Calculate the amount spent on food
Samu spent \( \frac{1}{8} \) of his money on food. Therefore, the amount spent on food is:
\[ \text{Amount spent on food} = \frac{1}{8}X \]

### Step 4: Calculate the total amount spent
The total amount spent on books and food is:
\[ \text{Total spent} = \frac{1}{4}X + \frac{1}{8}X \]
To add these fractions, we need a common denominator. The least common multiple of 4 and 8 is 8. Thus, we can rewrite \( \frac{1}{4}X \) as \( \frac{2}{8}X \):
\[ \text{Total spent} = \frac{2}{8}X + \frac{1}{8}X = \frac{3}{8}X \]

### Step 5: Calculate the remaining amount
According to the problem, after spending on books and food, Samu is left with 40. Therefore, we can write the equation:
\[ X - \frac{3}{8}X = 40 \]

### Step 6: Simplify the equation
This simplifies to:
\[ \frac{5}{8}X = 40 \]

### Step 7: Solve for \( X \)
To find \( X \), multiply both sides by \( \frac{8}{5} \):
\[ X = 40 \times \frac{8}{5} = 64 \]

### Step 8: Calculate the amount spent on food
Now that we know the total amount of money Samu had, we can calculate how much he spent on food:
\[ \text{Amount spent on food} = \frac{1}{8}X = \frac{1}{8} \times 64 = 8 \]

### Final Answer
Samu spent **8** on food.

---