A house and a shop were sold for Rs. 1 lakh each, In this transaction, the house sale resulted into 20% loss whereas the shop sale into 20% profit. The entire transaction resulted in :

Answer

To solve the problem step by step, we need to analyze the transactions involving the house and the shop.

### Step 1: Understand the Selling Prices
Both the house and the shop were sold for Rs. 1 lakh each.

- Selling Price (SP) of the house = Rs. 1,00,000
- Selling Price (SP) of the shop = Rs. 1,00,000

### Step 2: Calculate the Cost Price of the House
The house was sold at a 20% loss. This means that the Selling Price is 80% of the Cost Price (CP).

Let the Cost Price of the house be \( CP_H \).

\[ SP_H = CP_H - 0.20 \times CP_H = 0.80 \times CP_H \]

Substituting the Selling Price:

\[ 1,00,000 = 0.80 \times CP_H \]

Now, solve for \( CP_H \):

\[ CP_H = \frac{1,00,000}{0.80} = 1,25,000 \]

### Step 3: Calculate the Cost Price of the Shop
The shop was sold at a 20% profit. This means that the Selling Price is 120% of the Cost Price (CP).

Let the Cost Price of the shop be \( CP_S \).

\[ SP_S = CP_S + 0.20 \times CP_S = 1.20 \times CP_S \]

Substituting the Selling Price:

\[ 1,00,000 = 1.20 \times CP_S \]

Now, solve for \( CP_S \):

\[ CP_S = \frac{1,00,000}{1.20} = 83,333.33 \]

### Step 4: Calculate Total Cost Price and Total Selling Price
Now, we can calculate the total Cost Price (CP) and total Selling Price (SP) for both transactions.

- Total Cost Price (CP) = \( CP_H + CP_S \)

\[ Total \, CP = 1,25,000 + 83,333.33 = 2,08,333.33 \]

- Total Selling Price (SP) = \( SP_H + SP_S \)

\[ Total \, SP = 1,00,000 + 1,00,000 = 2,00,000 \]

### Step 5: Calculate the Overall Profit or Loss
To find the overall profit or loss, subtract the total Selling Price from the total Cost Price.

\[ Loss = Total \, CP - Total \, SP \]

\[ Loss = 2,08,333.33 - 2,00,000 = 8,333.33 \]

### Final Answer
The entire transaction resulted in a loss of Rs. 8,333.33.

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