An article is sold at a loss of 5%. If it is sold at Rs. 72 more, the...
Given information:
- The article is sold at a loss of 5%.
- If it is sold at Rs. 72 more, then there would be a profit of 4%.
Let's assume:
- The actual price of the article is Rs. X.
Calculating the loss:
- If the article is sold at a loss of 5%, it means it is sold at 95% of its actual price.
- So, the selling price (SP) at a loss of 5% is 95% of X.
- Selling price = (95/100) * X = 0.95X
Calculating the profit:
- If the article is sold at a profit of 4%, it means it is sold at 104% of its actual price.
- So, the selling price (SP) at a profit of 4% is 104% of X.
- Selling price = (104/100) * X = 1.04X
Given condition:
- If the article is sold at Rs. 72 more, then there would be a profit of 4%.
- So, the selling price (SP) at a profit of 4% after adding Rs. 72 is 1.04X + 72.
Equating the selling prices:
- According to the given condition, the selling prices in both cases are the same.
- 0.95X = 1.04X + 72
Solving the equation:
- Subtracting 0.95X from both sides, we get: 0 = 0.09X + 72
- Subtracting 72 from both sides, we get: -72 = 0.09X
- Dividing both sides by 0.09, we get: X = -72/0.09 = -800
Interpreting the result:
- The actual price of the article cannot be negative, so we have made an error in our calculations.
- Let's assume the actual price of the article is Rs. Y instead of X.
Calculating again:
- The selling price at a loss of 5% is 95% of Y, which is 0.95Y.
- The selling price at a profit of 4% after adding Rs. 72 is 1.04Y + 72.
Equating the selling prices:
- According to the given condition, the selling prices in both cases are the same.
- 0.95Y = 1.04Y + 72
Solving the equation:
- Subtracting 0.95Y from both sides, we get: 0 = 0.09Y + 72
- Subtracting 72 from both sides, we get: -72 = 0.09Y
- Dividing both sides by 0.09, we get: Y = -72/0.09 = -800
Interpreting the result:
- The actual price of the article cannot be negative, so we have made an error in our calculations again.
- Let's recheck the given information and conditions.
Correct calculation:
- The selling price at a loss of 5%
An article is sold at a loss of 5%. If it is sold at Rs. 72 more, the...
Let, the actual price of the article be Rs. 'x'.
The article is sold at a loss of 5%.
Selling price of the article = 95% of Rs. x or Rs. 0.95x
Given,
If it was sold at Rs. 72 more, then there would be a profit of 4%.
0.95x + 72 = 104% of x
0.95x + 72 = 1.04x
0.09x = 72
x = 800
Actual price of the item is Rs. 800.
Hence, answer option 4 is correct.