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Raju sold two fans for Rs. 990 each . On...

Raju sold two fans for Rs. 990 each . On selling one fan , he had a gain of `10%` and on selling other fan , he has a loss of `10%` .Find his gain or loss per cent in the whole transaction .

A

`1%` loss

B

`1%` gain

C

`2%` loss

D

`2%` gain

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will first determine the cost price (CP) of each fan based on the given selling prices and profit/loss percentages. ### Step 1: Determine the Selling Price (SP) of each fan Raju sold each fan for Rs. 990. ### Step 2: Calculate the Cost Price (CP) of the first fan The first fan was sold at a gain of 10%. Let the cost price of the first fan be \( CP_1 \). Using the formula for selling price with profit: \[ SP = CP + \text{Profit} \] \[ SP = CP_1 + 0.10 \times CP_1 = 1.10 \times CP_1 \] Given that \( SP = 990 \): \[ 990 = 1.10 \times CP_1 \] To find \( CP_1 \): \[ CP_1 = \frac{990}{1.10} = 900 \] ### Step 3: Calculate the Cost Price (CP) of the second fan The second fan was sold at a loss of 10%. Let the cost price of the second fan be \( CP_2 \). Using the formula for selling price with loss: \[ SP = CP - \text{Loss} \] \[ SP = CP_2 - 0.10 \times CP_2 = 0.90 \times CP_2 \] Given that \( SP = 990 \): \[ 990 = 0.90 \times CP_2 \] To find \( CP_2 \): \[ CP_2 = \frac{990}{0.90} = 1100 \] ### Step 4: Calculate the total Cost Price (CP) of both fans Now, we can find the total cost price of both fans: \[ \text{Total CP} = CP_1 + CP_2 = 900 + 1100 = 2000 \] ### Step 5: Calculate the total Selling Price (SP) of both fans The total selling price of both fans: \[ \text{Total SP} = 990 + 990 = 1980 \] ### Step 6: Determine the overall gain or loss To find the overall gain or loss: \[ \text{Total Loss} = \text{Total CP} - \text{Total SP} = 2000 - 1980 = 20 \] ### Step 7: Calculate the percentage of loss The percentage of loss can be calculated using the formula: \[ \text{Percentage of Loss} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \] Substituting the values: \[ \text{Percentage of Loss} = \left( \frac{20}{2000} \right) \times 100 = 1\% \] ### Final Answer Raju incurred a loss of **1%** in the whole transaction. ---
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