Johny calculates his profit at cost price while Jini at selling price. If cost price is same for all and everyone Calculate their profit as 10%. Find ratio of selling price.

Options

A. A)`100:111`
B. B)`10:11`
C. C)`10:101`
D. D)`99:100`

Answer

To solve the problem, we need to calculate the selling prices for both Johny and Jini based on their respective profit calculations and then find the ratio of these selling prices.

### Step-by-Step Solution:

1. **Understanding the Profit Calculation**:
- Johny calculates his profit based on the cost price (CP).
- Jini calculates her profit based on the selling price (SP).
- Both have a profit of 10%.

2. **Calculating Selling Price for Johny**:
- Let the cost price (CP) be 100 (for simplicity).
- Since Johny calculates profit at cost price, his selling price (SP) will be:
\[ SP_{Johny} = CP + Profit = 100 + 10\% \text{ of } 100 = 100 + 10 = 110 \]

3. **Calculating Selling Price for Jini**:
- Jini calculates her profit at selling price.
- Let the selling price (SP) be 100.
- Since she calculates profit based on SP, we can express the cost price as:
\[ CP = SP - Profit = 100 - 10\% \text{ of } 100 = 100 - 10 = 90 \]

4. **Setting Cost Prices Equal**:
- According to the problem, the cost price is the same for both Johny and Jini.
- So we set the cost prices equal:
\[ 100 = 90 \]
- This is incorrect. We need to express the selling price of Jini in terms of the cost price of Johny.

5. **Finding the Ratio of Selling Prices**:
- Now, we know:
- Selling Price of Johny (SP_J) = 110
- Selling Price of Jini (SP_Ji) = 100
- To find the ratio of their selling prices:
\[ \text{Ratio} = \frac{SP_{Johny}}{SP_{Jini}} = \frac{110}{100} = \frac{11}{10} \]

6. **Final Ratio**:
- The ratio of selling prices of Johny to Jini is:
\[ 11:10 \]

### Final Answer:
The ratio of selling prices of Johny and Jini is **11:10**.