Ritu's total expenditure on a trip is divided among travel expenses, accommodation expenses, and shopping expenses in the ratio of 5 : 4 : 3 respectively.

- Out of the travel expenses, 25\% is spent on bus tickets, 60\% on air tickets, and the remaining travel expenses are saved.
- All accommodation expenses are spent on hotels.
- Of the shopping expenses, 50\% is spent on tax-free products, 47\frac{2}{9}\% on footpath shopping, and the rest are saved.

If the total amount saved during the trip is Rs. 17,500, what is Ritu's total expenditure on the trip?

Question

Ritu's total expenditure on a trip is divided among travel expenses, accommodation expenses, and shopping expenses in the ratio of 5 : 4 : 3 respectively.

- Out of the travel expenses, 25\% is spent on bus tickets, 60\% on air tickets, and the remaining travel expenses are saved.
- All accommodation expenses are spent on hotels.
- Of the shopping expenses, 50\% is spent on tax-free products, 47\frac{2}{9}\% on footpath shopping, and the rest are saved.

If the total amount saved during the trip is Rs. 17,500, what is Ritu's total expenditure on the trip?

Accepted Answer

**Solution:**

1. Let the total expenditure be $ x $.

2. Given the ratio of travel : accommodation : shopping expenses = 5 : 4 : 3.
   - Travel expenses = $ \frac{5}{12}x $
   - Accommodation expenses = $ \frac{4}{12}x = \frac{1}{3}x $
   - Shopping expenses = $ \frac{3}{12}x = \frac{1}{4}x $

3. Savings from travel expenses:
   - Bus tickets = 25\% of travel expenses = $ 0.25 \times \frac{5}{12}x = \frac{5}{48}x $
   - Air tickets = 60\% of travel expenses = $ 0.60 \times \frac{5}{12}x = \frac{1}{4}x $
   - Remaining travel expenses saved = $ \frac{5}{12}x - \left( \frac{5}{48}x + \frac{1}{4}x \right) $

Calculate saved travel expenses:
   $$
   \frac{5}{12}x - \left( \frac{5}{48}x + \frac{1}{4}x \right) = \frac{5}{12}x - \left( \frac{5}{48}x + \frac{12}{48}x \right) = \frac{5}{12}x - \frac{17}{48}x = \frac{20}{48}x - \frac{17}{48}x = \frac{3}{48}x = \frac{1}{16}x
   $$

4. Accommodation expenses are fully spent on hotels, so no savings here.

5. Savings from shopping expenses:
   - Tax-free products = 50\% of shopping expenses = $ 0.50 \times \frac{1}{4}x = \frac{1}{8}x $
   - Footpath shopping = 47\frac{2}{9}\% = $ \frac{425}{900} = \frac{17}{36} $ of shopping expenses
     $ = \frac{17}{36} \times \frac{1}{4}x = \frac{17}{144}x $
   - Remaining shopping expenses saved = $ \frac{1}{4}x - \left( \frac{1}{8}x + \frac{17}{144}x \right) $

Calculate saved shopping expenses:
   $$
   \frac{1}{4}x - \left( \frac{1}{8}x + \frac{17}{144}x \right) = \frac{36}{144}x - \left( \frac{18}{144}x + \frac{17}{144}x \right) = \frac{36}{144}x - \frac{35}{144}x = \frac{1}{144}x
   $$

6. Total savings = savings from travel + savings from shopping =
   $$
   \frac{1}{16}x + \frac{1}{144}x = \frac{9}{144}x + \frac{1}{144}x = \frac{10}{144}x = \frac{5}{72}x
   $$

7. Given total savings = Rs. 17,500
   $$
   \frac{5}{72}x = 17500 \implies x = 17500 \times \frac{72}{5} = 17500 \times 14.4 = 252000
   $$

**Answer:** Rs. 252,000

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