Calculating Total Gain or Loss on Jewellery Sets

This problem involves calculating the profit and loss on individual items and then finding the overall profit or loss for the entire transaction. We need to determine the selling price for each jewellery set and then compare the total selling price with the total cost price.

Step-by-Step Calculation of Selling Prices

Mona purchased two jewellery sets, each for Rs. 4,000. This is the cost price (CP) for each set.

• Cost Price of the first set = Rs. 4,000
• Cost Price of the second set = Rs. 4,000

Calculating Selling Price for the First Set (with Gain):

The first set was sold at an 8% gain.

Gain amount on the first set is 8% of the cost price:

\(\text{Gain amount} = 8\% \text{ of Rs. } 4000\)

\(\text{Gain amount} = \frac{8}{100} \times 4000\)

\(\text{Gain amount} = 8 \times 40\)

\(\text{Gain amount} = \text{Rs. } 320\)

The Selling Price (SP) is the Cost Price plus the Gain:

\(\text{Selling Price (First Set)} = \text{Cost Price} + \text{Gain amount}\)

\(\text{Selling Price (First Set)} = 4000 + 320\)

\(\text{Selling Price (First Set)} = \text{Rs. } 4320\)

Calculating Selling Price for the Second Set (with Loss):

The second set was sold at a 6% loss.

Loss amount on the second set is 6% of the cost price:

\(\text{Loss amount} = 6\% \text{ of Rs. } 4000\)

\(\text{Loss amount} = \frac{6}{100} \times 4000\)

\(\text{Loss amount} = 6 \times 40\)

\(\text{Loss amount} = \text{Rs. } 240\)

The Selling Price (SP) is the Cost Price minus the Loss:

\(\text{Selling Price (Second Set)} = \text{Cost Price} - \text{Loss amount}\)

\(\text{Selling Price (Second Set)} = 4000 - 240\)

\(\text{Selling Price (Second Set)} = \text{Rs. } 3760\)

Calculating Total Cost Price and Total Selling Price

Now, let's find the total cost price and total selling price for both sets of jewellery.

Total Cost Price = Cost Price of First Set + Cost Price of Second Set

\(\text{Total CP} = 4000 + 4000\)

\(\text{Total CP} = \text{Rs. } 8000\)

Total Selling Price = Selling Price of First Set + Selling Price of Second Set

\(\text{Total SP} = 4320 + 3760\)

\(\text{Total SP} = \text{Rs. } 8080\)

Determining Overall Gain or Loss

To find the total gain or loss in the whole transaction, we compare the total selling price with the total cost price.

• If Total SP > Total CP, there is a Gain.
• If Total SP < Total CP, there is a Loss.
• If Total SP = Total CP, there is no gain or loss.

In this case, Total SP (Rs. 8080) is greater than Total CP (Rs. 8000).

So, there is an overall gain.

Overall Gain = Total Selling Price - Total Cost Price

\(\text{Overall Gain} = 8080 - 8000\)

\(\text{Overall Gain} = \text{Rs. } 80\)

Mona's total gain in this whole transaction is Rs. 80.

Therefore, the total result of the transaction is a gain of Rs. 80.

Revision Table: Profit and Loss Concepts

Additional Information on Profit and Loss Calculations

When dealing with multiple items in a single transaction, it's crucial to calculate the total cost price and total selling price for all items combined before determining the overall gain or loss. You cannot simply average the individual profit/loss percentages.

Formulas for SP when percentage gain or loss is given:

• If there is a gain of r%, Selling Price \( = \text{CP} \times \left(1 + \frac{r}{100}\right) \).
• If there is a loss of r%, Selling Price \( = \text{CP} \times \left(1 - \frac{r}{100}\right) \).

Using these formulas for the problem:

• SP (First Set) = \(4000 \times \left(1 + \frac{8}{100}\right) = 4000 \times \left(\frac{108}{100}\right) = 40 \times 108 = 4320\)
• SP (Second Set) = \(4000 \times \left(1 - \frac{6}{100}\right) = 4000 \times \left(\frac{94}{100}\right) = 40 \times 94 = 3760\)

These results match the calculations done earlier, confirming the total gain of Rs. 80.