Let's analyze the problem step-by-step.
Problem Restatement
- A man sells a TV set for Rs. 30 and makes a profit of 20%.
- He sells another TV set at a loss of 10%.
- Overall, he neither gains nor loses on the two transactions combined.
- We need to find the selling price of the second TV set.
Step 1: Find the cost price of the first TV
- Selling price (SP1) = Rs. 30
- Profit = 20%
Using the formula for profit:
\text{SP}=\text{CP}+\text{Profit}=\text{CP}\times (1+\frac{\text{Profit%}}{100})
30=\text{CP}_1\times (1+\frac{20}{100})=\text{CP}_1\times 1.2
\text{CP}_1=\frac{30}{1.2}=25
So, the cost price of the first TV is Rs. 25.
Step 2: Let the cost price of the second TV be \text{CP}_2.
Loss on second TV = 10% Selling price of second TV is:
\text{SP}_2=\text{CP}_2\times (1-\frac{10}{100})=0.9\times \text{CP}_2
Step 3: Use the condition of no overall gain or loss
Total cost price = \text{CP}_1+\text{CP}_2=25+\text{CP}_2 Total selling price = \text{SP}_1+\text{SP}_2=30+0.9\times \text{CP}_2 Since there is no overall gain or loss:
\text{Total SP}=\text{Total CP}
30+0.9\times \text{CP}_2=25+\text{CP}_2
30-25=\text{CP}_2-0.9\times \text{CP}_2
5=0.1\times \text{CP}_2
\text{CP}_2=\frac{5}{0.1}=50
Step 4: Find the selling price of the second TV
\text{SP}_2=0.9\times 50=45
Final Answer:
The selling price of the second TV set is Rs. 45.
