Lata spent `20%` of the money she had on jeans and `5%` on a pair of slippers. She was left with Rs2700. How much money did she have in the beginning?

Answer

To solve the problem step by step, we will follow the mathematical reasoning outlined in the video transcript.

### Step 1: Define the initial amount
Let \( X \) be the total amount of money Lata had in the beginning.

**Hint:** When dealing with problems involving percentages, it's often helpful to define the total amount as a variable.

### Step 2: Calculate the amounts spent
Lata spent:
- 20% of \( X \) on jeans
- 5% of \( X \) on slippers

The total amount spent can be expressed as:
\[ \text{Total spent} = 20\% \text{ of } X + 5\% \text{ of } X = \frac{20}{100}X + \frac{5}{100}X = \frac{25}{100}X = \frac{1}{4}X \]

**Hint:** To combine percentages, convert them to fractions of the total amount.

### Step 3: Calculate the remaining amount
After spending on jeans and slippers, Lata is left with Rs 2700. Therefore, we can set up the equation:
\[ X - \left(\frac{25}{100}X\right) = 2700 \]

**Hint:** The remaining amount is what is left after subtracting the total spent from the initial amount.

### Step 4: Simplify the equation
We can simplify the equation:
\[ X - \frac{25}{100}X = 2700 \]
This simplifies to:
\[ \frac{75}{100}X = 2700 \]
or
\[ \frac{3}{4}X = 2700 \]

**Hint:** When simplifying, make sure to combine like terms and express them in a simple fraction form.

### Step 5: Solve for \( X \)
To find \( X \), multiply both sides by the reciprocal of \( \frac{3}{4} \):
\[ X = 2700 \times \frac{4}{3} \]
Calculating this gives:
\[ X = 2700 \times \frac{4}{3} = 2700 \times 1.3333 = 3600 \]

**Hint:** When multiplying by a fraction, remember to multiply the numerator and divide by the denominator.

### Step 6: Conclusion
Thus, the amount of money Lata had in the beginning is Rs 3600.

**Final Answer:** Lata had Rs 3600 in the beginning.

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