Multiple Transactions | MCQs

Explanation

1. One-third of the goods are sold at a 10% profit, so the profit from this portion is:

(1/3) x 10% = 3.33%

2. Another one-third of the goods are sold at a 20% profit, so the profit from this portion is:

(1/3) x 20% = 6.67%

3. The rest (1/3) of the goods are sold at a 6% loss, so the loss from this portion is:

(1/3) x (-6%) = -2%

4. Add up the profits and losses to find the overall profit percentage:

3.33% + 6.67% - 2% = 8%

So, the shopkeeper's overall profit percentage is 8%.

Explanation

To determine the overall percentage gain or loss in the transaction, we first need to establish the cost prices of the two chairs and then calculate the net gain or loss.

**Chair 1:**

- Selling Price (SP) = Rs. 1,200

- Gain = 20%

LetC_1 be the cost price of the first chair.

Since he gained 20%, we use the formula for the selling price:

SP = C_1 + (0.20 times C_1

1,200 = 1.20 times C_1

C_1 = frac{1,200}{1.20} 

C_1 = 1,000 

So, the cost price of the first chair is Rs. 1,000.

**Chair 2:**

- Selling Price (SP) = Rs. 1,200

- Loss = 20%

Let ( C_2 ) be the cost price of the second chair.

Since he lost 20%, we use the formula for selling price:

SP = C_2 - (0.20 times C_2)

1,200 = 0.80 times C_2

C_2 = frac{1,200}{0.80}

 C_2 = 1,500 

So, the cost price of the second chair is Rs. 1,500.

**Total Cost Price and Total Selling Price:**

- Total Cost Price =  C_1 + C_2 = 1,000 + 1,500 = 2,500 

- Total Selling Price = Rs. 1,200 + Rs. 1,200 = Rs. 2,400

**Net Loss:**

text{Net Loss} = text{Total Cost Price} - text{Total Selling Price} 

ext{Net Loss} = 2,500 - 2,400 = 100 

**Percentage Loss:**

text{Percentage Loss} = left( frac{text{Net Loss}}{text{Total Cost Price}} right) times 100

text{Percentage Loss} =  left(  frac{100}{2,500}  right)  times 100 

text{Percentage Loss} = 4%