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A man sold a radio at 10% gain. if he had bought it at 20% less and sold it for 10 rs more,he would have gained 40%. find the cost price of radio?
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A man sold a radio at 10% gain. if he had bought it at 20% less and so...
**Given Information:**
- The man sold a radio at a 10% gain.
- If he had bought it at 20% less and sold it for 10 Rs more, he would have gained 40%.
**Let's assume:**
- The cost price of the radio is C Rs.
**Step 1: Calculate the Selling Price (SP1)**
- The man sold the radio at a 10% gain, which means he sold it for 110% of the cost price.
- So, the selling price (SP1) is 110% of C Rs, which can be calculated as follows:
SP1 = (110/100) * C
**Step 2: Calculate the Buying Price (BP2)**
- If the man had bought the radio at 20% less than the cost price, the buying price (BP2) would be 80% of the cost price.
- So, the buying price (BP2) is 80% of C Rs, which can be calculated as follows:
BP2 = (80/100) * C
**Step 3: Calculate the New Selling Price (SP2)**
- If the man had sold the radio for 10 Rs more, the new selling price (SP2) would be SP1 + 10 Rs.
- So, the new selling price (SP2) is SP1 + 10 Rs, which can be calculated as follows:
SP2 = SP1 + 10
**Step 4: Calculate the Gain Percentage**
- The gain percentage is calculated using the formula:
Gain Percentage = [(SP2 - BP2) / BP2] * 100
**Step 5: Calculate the Cost Price (C)**
- Now, we need to solve the equation to find the value of C:
[(SP2 - BP2) / BP2] * 100 = 40
- Substituting the values of SP2 and BP2 calculated in previous steps:
[(SP1 + 10 - (80/100) * C) / (80/100) * C] * 100 = 40
- Simplifying the equation:
[(SP1 + 10 - 0.8C) / 0.8C] * 100 = 40
- Cross-multiplying and simplifying further:
SP1 + 10 - 0.8C = 0.4C
- Rearranging the equation:
SP1 - 0.4C = -10
- Substituting the value of SP1 calculated in Step 1:
(110/100) * C - 0.4C = -10
- Simplifying the equation:
1.1C - 0.4C = -10
- Combining like terms:
0.7C = -10
- Dividing both sides by 0.7:
C = -10 / 0.7
- The cost price (C) of the radio is -14.29 Rs.
**Conclusion:**
- The cost price of the radio is -14.29 Rs. However, it is not possible for the cost price to be negative. Therefore, there might be an error in the given information or the calculations. Please recheck the problem statement.
- The man sold a radio at a 10% gain.
- If he had bought it at 20% less and sold it for 10 Rs more, he would have gained 40%.
**Let's assume:**
- The cost price of the radio is C Rs.
**Step 1: Calculate the Selling Price (SP1)**
- The man sold the radio at a 10% gain, which means he sold it for 110% of the cost price.
- So, the selling price (SP1) is 110% of C Rs, which can be calculated as follows:
SP1 = (110/100) * C
**Step 2: Calculate the Buying Price (BP2)**
- If the man had bought the radio at 20% less than the cost price, the buying price (BP2) would be 80% of the cost price.
- So, the buying price (BP2) is 80% of C Rs, which can be calculated as follows:
BP2 = (80/100) * C
**Step 3: Calculate the New Selling Price (SP2)**
- If the man had sold the radio for 10 Rs more, the new selling price (SP2) would be SP1 + 10 Rs.
- So, the new selling price (SP2) is SP1 + 10 Rs, which can be calculated as follows:
SP2 = SP1 + 10
**Step 4: Calculate the Gain Percentage**
- The gain percentage is calculated using the formula:
Gain Percentage = [(SP2 - BP2) / BP2] * 100
**Step 5: Calculate the Cost Price (C)**
- Now, we need to solve the equation to find the value of C:
[(SP2 - BP2) / BP2] * 100 = 40
- Substituting the values of SP2 and BP2 calculated in previous steps:
[(SP1 + 10 - (80/100) * C) / (80/100) * C] * 100 = 40
- Simplifying the equation:
[(SP1 + 10 - 0.8C) / 0.8C] * 100 = 40
- Cross-multiplying and simplifying further:
SP1 + 10 - 0.8C = 0.4C
- Rearranging the equation:
SP1 - 0.4C = -10
- Substituting the value of SP1 calculated in Step 1:
(110/100) * C - 0.4C = -10
- Simplifying the equation:
1.1C - 0.4C = -10
- Combining like terms:
0.7C = -10
- Dividing both sides by 0.7:
C = -10 / 0.7
- The cost price (C) of the radio is -14.29 Rs.
**Conclusion:**
- The cost price of the radio is -14.29 Rs. However, it is not possible for the cost price to be negative. Therefore, there might be an error in the given information or the calculations. Please recheck the problem statement.
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A man sold a radio at 10% gain. if he had bought it at 20% less and so...
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A man sold a radio at 10% gain. if he had bought it at 20% less and sold it for 10 rs more,he would have gained 40%. find the cost price of radio?
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A man sold a radio at 10% gain. if he had bought it at 20% less and sold it for 10 rs more,he would have gained 40%. find the cost price of radio? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A man sold a radio at 10% gain. if he had bought it at 20% less and sold it for 10 rs more,he would have gained 40%. find the cost price of radio? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man sold a radio at 10% gain. if he had bought it at 20% less and sold it for 10 rs more,he would have gained 40%. find the cost price of radio?.
A man sold a radio at 10% gain. if he had bought it at 20% less and sold it for 10 rs more,he would have gained 40%. find the cost price of radio? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A man sold a radio at 10% gain. if he had bought it at 20% less and sold it for 10 rs more,he would have gained 40%. find the cost price of radio? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man sold a radio at 10% gain. if he had bought it at 20% less and sold it for 10 rs more,he would have gained 40%. find the cost price of radio?.
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