Calculating Loss Percentage for a Table Sale

Let's analyze the given information about the table sale to determine the loss percentage.

• The selling price (SP) of the table is given as Rs. 16,870.
• The shopkeeper suffered a loss of Rs. 1,080 on this sale.
• We need to find the loss percentage, rounded off to one decimal place.

Determining the Cost Price (CP)

When a loss occurs, the cost price is the selling price plus the amount of loss. This is because the item was bought for more than it was sold for, with the difference being the loss.

The formula to find the cost price (CP) when there is a loss is:

$\text{CP} = \text{SP} + \text{Loss}$

Let's substitute the given values:

$\text{CP} = \text{Rs. } 16,870 + \text{Rs. } 1,080$

Calculating the sum:

$\text{CP} = \text{Rs. } 17,950$

So, the cost price of the table was Rs. 17,950.

Calculating the Loss Percentage

The loss percentage is calculated based on the cost price. It tells us what fraction of the cost price the loss represents, expressed as a percentage.

The formula for calculating loss percentage is:

$\text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\%$

We know the Loss (Rs. 1,080) and we have calculated the CP (Rs. 17,950). Now, let's plug these values into the formula:

$\text{Loss Percentage} = \left( \frac{1080}{17950} \right) \times 100\%$

First, perform the division:

$\frac{1080}{17950} \approx 0.060167131$

Now, multiply by 100% to get the percentage:

$\text{Loss Percentage} \approx 0.060167131 \times 100\% \approx 6.0167131\%$

Rounding to One Decimal Place

The question asks for the loss percentage rounded off to one decimal place. We have approximately 6.0167%. To round to one decimal place, we look at the second decimal place. The second decimal place is 1.

• If the second decimal place is 5 or greater, we round up the first decimal place.
• If the second decimal place is less than 5, we keep the first decimal place as it is.

Since 1 is less than 5, we keep the first decimal place (0) as it is.

Rounded Loss Percentage $\approx 6.0\%$

Let's summarise the calculation steps:

Therefore, the loss percentage, rounded off to one decimal place, is 6.0%.

Revision Table: Profit and Loss Basics

Additional Information on Percentage Calculations

Understanding percentage calculations is fundamental in various financial and mathematical problems. A percentage is simply a way of expressing a fraction with a denominator of 100. The formula for percentage change (like profit or loss percentage) always relates the change (profit or loss amount) to the original value (Cost Price in this case).

When dealing with rounding:

• To round to 'n' decimal places, look at the digit in the (n+1)th decimal place.
• If this digit is 5 or greater, increase the digit in the nth decimal place by 1 and drop all subsequent digits.
• If this digit is less than 5, keep the digit in the nth decimal place as it is and drop all subsequent digits.

In our table sale example, we rounded 6.0167% to one decimal place (n=1). We looked at the second decimal place (n+1=2), which was 1. Since 1 < 5, we kept the first decimal place (0) as it was, resulting in 6.0%.