Naman purchased two pairs of shoes. On the Puma shoes, he received a 40\% discount, while on the Nike shoes, he got successive discounts of 20\% and 20\%. The marked price of the Puma shoes is 25\% higher than that of the Nike shoes. Additionally, the shopkeeper charged a 5\% tax on the total selling price of both shoes combined. If the total amount paid by Naman is Rs. 5838, what is the marked price of the Puma shoes?

Question

Accepted Answer

**Solution:**

1. Let the marked price of Nike shoes be $ x $. Then, the marked price of Puma shoes is $ 1.25x $ (since it is 25\% more).

2. Calculate the selling price of Puma shoes after 40\% discount:
   $$
  $ \text{Selling price of Puma} = 1.25x \times (1 - 0.40) = 1.25x \times 0.60 = 0.75x$
   $$

3. Calculate the selling price of Nike shoes after successive discounts of 20\% and 20\%:
   - After first 20\% discount: $ $x \times 0.80 = 0.8x $$
   - After second 20\% discount on the reduced price: $ $0.8x \times 0.80 = 0.64x$ $

4. Total selling price before tax:
   $$
   0.75x + 0.64x = 1.39x
   $$

5. Shopkeeper charges 5\% tax on the total selling price, so total amount paid is:
   $$
 $  1.39x \times 1.05 = 1.4595x$
   $$

6. Given total amount paid is Rs. 5838:
   $$
  $ 1.4595x = 5838 \implies x = \frac{5838}{1.4595} \approx 4000$
   $$

7. Marked price of Puma shoes:
   $$
 $  1.25x = 1.25 \times 4000 = 5000$
   $$

**Answer:** Rs. 5000

Answer

Answer

Answer

Answer