A merchant sells a computer for ₹Z, incurring a loss of 12%. Afterwards, the merchant lists a second unit at a price equal to 0.9Z and provides a 10% discount on that listed price. What is the overall percentage loss sustained on the second unit compared to the original cost price?

Correct Answer: 28.7%

Step-by-Step Explanation:

Step 1: Understand the Cost Price (CP) and Selling Price of the first computer

Let the original Cost Price of the computer be CP.

The merchant sells the first computer for ₹Z at a loss of 12%.

Therefore, the relationship between the selling price Z and the cost price CP is given by:

$Z=CP\times (1-0.12)=0.88\times CP$

From this, we can express the Cost Price in terms of Z:

$CP=\frac{Z}{0.88}$

Step 2: Calculate the Selling Price of the second unit

The second unit is listed at a price equal to 0.9Z.

A discount of 10% is given on this listed price.

So, the final selling price of the second unit (SP₂) is:

$S{P}_2=0.9Z\times (1-0.10)=0.9Z\times 0.9=0.81Z$

Step 3: Determine the overall percentage loss on the second unit compared to the original Cost Price

The loss on the second unit is the difference between the Cost Price (CP) and the final Selling Price (SP₂):

$\text{Loss}=CP-S{P}_2=\frac{Z}{0.88}-0.81Z=Z\times (\frac{1}{0.88}-0.81)$

Now, calculate the percentage loss relative to the original Cost Price CP:

$\text{Percentage Loss}=\frac{\text{Loss}}{CP}\times 100$

$\text{Percentage Loss}=\frac{\frac{Z}{0.88}-0.81Z}{\frac{Z}{0.88}}$

Calculate the product:

$0.81\times 0.88=0.7128$

Substitute this value back into the percentage loss formula:

$\text{Percentage Loss}=(1-0.7128)\times 100=0.2872\times 100=28.72\%$

Rounding to one decimal place gives 28.7%.