Analyzing the Travel Expenses Problem
This problem involves calculating an initial budget based on changes in average daily expenses due to an extended stay. We need to find the total amount sanctioned to Sonal.
Setting Up the Equations
Let the total amount sanctioned (budget) be B.
- Initial duration = 16 days.
- Initial average daily allowance = $\frac{B}{16}$.
- Extended duration = 16 days + 8 days = 24 days.
- New average daily allowance = $\frac{B}{24}$.
- The difference in average daily allowance is given as ₹80.
Calculating the Initial Sanctioned Amount
- Set up the equation based on the difference in average daily allowance:
$ \frac{B}{16} - \frac{B}{24} = 80 $
- Find a common denominator for the fractions (which is 48):
$ B \left( \frac{1}{16} - \frac{1}{24} \right) = 80 $
$ B \left( \frac{3}{48} - \frac{2}{48} \right) = 80 $
- Simplify the expression:
$ B \left( \frac{1}{48} \right) = 80 $
- Solve for B (the total sanctioned amount):
$ B = 80 \times 48 $
$ B = 3840 $
Therefore, the initial amount sanctioned to Sonal was ₹3,840.
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