Directions: Calculate the marked price using the information below.

A shopper buys two travel backpacks. The first backpack is offered at a 36% discount, while the second backpack receives successive discounts of 10% and 20%. The marked price of the first backpack is 25% higher than that of the second backpack. A 5% tax is added to the combined discounted prices, and the shopper pays Rs. 6384 in total. What is the marked price of the first backpack?

The correct option is Rs. 5000.

To find the marked price of the first backpack, let us define the marked prices of both backpacks using algebraic variables.
Let the marked price of the second backpack be $M_2$ and the marked price of the first backpack be $M_1$.

According to the question, the marked price of the first backpack is 25% higher than that of the second backpack.

$M_1=M_2+0.25\times M_2=1.25\times M_2$

Step 1: Calculate the discounted selling price of the first backpack.
The first backpack is offered at a 36% discount.

Selling Price of 1st Backpack = $M_1\times (1-0.36)=0.64\times M_1$

Substituting $M_1=1.25\times M_2$ into this equation gives:

Selling Price of 1st Backpack = $0.64\times 1.25\times M_2=0.80\times M_2$

Step 2: Calculate the discounted selling price of the second backpack.
The second backpack receives successive discounts of 10% and 20%.

Selling Price of 2nd Backpack = $M_2\times (1-0.10)\times (1-0.20)$

$=M_2\times 0.90\times 0.80=0.72\times M_2$

Step 3: Determine the combined discounted price of both backpacks.

Combined Discounted Price = $0.80\times M_2+0.72\times M_2=1.52\times M_2$

Step 4: Include tax to find the value of $M_2$.
A 5% tax is added to the combined discounted price, making the final total Rs. 6384.

Total Paid = $\text{Combined Discounted Price}\times (1+0.05)$

$6384=1.52\times M_2\times 1.05$

$6384=1.596\times M_2$

$M_2=\frac{6384}{1.596}=4000$

Step 5: Calculate the marked price of the first backpack ($M_1$).

$M_1=1.25\times M_2=1.25\times 4000=5000$

Thus, the marked price of the first backpack is Rs. 5000.