Ram sold two horses at the same price. In one he gets a profit of 10% and in the other he gets a loss of 10%. Then Ram gets

Options

A. 1% profit
B. no loss no profit
C. 2% loss
D. 1% loss

Answer

To solve the problem step by step, we need to analyze the situation where Ram sells two horses at the same price, one at a profit of 10% and the other at a loss of 10%.

### Step-by-Step Solution:

1. **Let the Selling Price (SP) of each horse be 'S'.**
- Since both horses are sold at the same price, we denote the selling price of each horse as S.

2. **Calculate the Cost Price (CP) of the first horse (with a profit of 10%).**
- If Ram sells the first horse at a profit of 10%, then:
\[ SP = CP_1 + (10\% \text{ of } CP_1) \]
\[ S = CP_1 + 0.1 \times CP_1 \]
\[ S = 1.1 \times CP_1 \]
\[ CP_1 = \frac{S}{1.1} \]

3. **Calculate the Cost Price (CP) of the second horse (with a loss of 10%).**
- If Ram sells the second horse at a loss of 10%, then:
\[ SP = CP_2 - (10\% \text{ of } CP_2) \]
\[ S = CP_2 - 0.1 \times CP_2 \]
\[ S = 0.9 \times CP_2 \]
\[ CP_2 = \frac{S}{0.9} \]

4. **Calculate the total Cost Price (CP) of both horses.**
- Total CP = CP_1 + CP_2
- Substitute the values from steps 2 and 3:
\[ Total \, CP = \frac{S}{1.1} + \frac{S}{0.9} \]

5. **Find a common denominator to add the two fractions.**
- The common denominator of 1.1 and 0.9 is 0.99 (which is 11/10 and 9/10 respectively).
- Rewrite the fractions:
\[ Total \, CP = \frac{S \times 0.9}{0.99} + \frac{S \times 1.1}{0.99} \]
\[ Total \, CP = \frac{0.9S + 1.1S}{0.99} \]
\[ Total \, CP = \frac{2S}{0.99} \]

6. **Calculate the overall profit or loss.**
- Total SP from selling both horses = S + S = 2S.
- Total CP = \(\frac{2S}{0.99}\).
- To find the profit or loss, we compare Total SP and Total CP:
\[ Profit/Loss = Total \, SP - Total \, CP \]
\[ Profit/Loss = 2S - \frac{2S}{0.99} \]
\[ Profit/Loss = 2S \left(1 - \frac{1}{0.99}\right) \]
\[ Profit/Loss = 2S \left(\frac{0.01}{0.99}\right) \]

7. **Calculate the percentage of profit or loss.**
- The overall loss percentage can be calculated as:
\[ Loss \% = \left(\frac{Loss}{Total \, CP}\right) \times 100 \]
- Substitute the values:
\[ Loss \% = \left(\frac{2S \left(\frac{0.01}{0.99}\right)}{\frac{2S}{0.99}}\right) \times 100 \]
\[ Loss \% = 1\% \]

### Conclusion:
Ram incurs a net loss of 1%.