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.