Calculating Rani's Total Amount

This problem involves finding the original amount when a percentage of it and the corresponding value are known.

Problem Setup

• Let the total amount Rani had be represented by $A$.
• Rani spent $6.25\%$ of this amount.
• The expenditure amounted to ₹75.

Mathematical Equation

We can express the given information as an equation:

$6.25\% \times A = ₹75$

Solving for the Total Amount

To find the total amount $A$, we first convert the percentage to a decimal or a fraction.

As a decimal: $6.25\% = \frac{6.25}{100} = 0.0625$.

The equation becomes:

$0.0625 \times A = 75$

Now, we solve for $A$ by dividing the expenditure by the decimal percentage:

$A = \frac{75}{0.0625}$

Alternative Calculation using Fractions

Alternatively, we can convert $6.25\%$ to a fraction:

$6.25\% = \frac{6.25}{100} = \frac{625}{10000} = \frac{1}{16}$

The equation is:

$\frac{1}{16} \times A = 75$

Solving for $A$:

$A = 75 \times 16$

Final Calculation

Performing the multiplication:

$A = 75 \times 16 = 1200$

Therefore, Rani had ₹1200.