After spending 1/4th of pocket money on chocolates and 1/8th on pizza, a girl is left with Rs.40. How much money did she have at first?

Let's denote the total pocket money the girl had initially as \( x \).

### Step 1: Understand the problem
- The girl spends \( \frac{1}{4} \) of her pocket money on chocolates.
- She spends \( \frac{1}{8} \) of her pocket money on pizza.
- After these expenses, she is left with Rs. 40.

### Step 2: Set up the equation
The amount of money left after spending can be written as:
\[
\text{Remaining money} = x - \left(\frac{1}{4}x + \frac{1}{8}x\right) = 40
\]

### Step 3: Simplify the expression
First, combine the fractions:
\[
\frac{1}{4}x + \frac{1}{8}x = \frac{2}{8}x + \frac{1}{8}x = \frac{3}{8}x
\]
So, the equation becomes:
\[
x - \frac{3}{8}x = 40
\]

### Step 4: Solve the equation
To solve for \( x \), factor out \( x \) from the left side:
\[
\left(1 - \frac{3}{8}\right)x = 40
\]

\[
\frac{5}{8}x = 40
\]

Now, solve for \( x \) by multiplying both sides by \( \frac{8}{5} \):
\[
x = 40 \times \frac{8}{5} = \frac{320}{5} = 64
\]

### Conclusion
The girl originally had **Rs. 64**.

Would you like more details or have any questions about this solution?

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### Related Questions:

1. How can we solve similar problems involving fractions of amounts?
2. What if she spent a different fraction on pizza?
3. How can we express the remaining amount as a fraction of the total?
4. What if she spent money on another item before pizza?
5. How do you approach word problems involving money and fractions?

### Tip:
When solving problems involving fractions of an amount, carefully set up the equation to express the remaining amount after each expense. Simplifying the fractions step-by-step will help in solving the equation accurately.

Learn how to solve a money word problem involving fractions. Understand how to calculate the initial amount of money a girl had, given that she spent 1/4th on chocolates and 1/8th on pizza, leaving Rs. 40 remaining. Suitable for students in Grades 5-7.

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