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A person bought a cycle and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs. 55 more, he would have had a profit of 40%. Find the profit percentage if he sold the cycle at Rs. 320.
- a)20%
- b)28%
- c)18%
- d)25%
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A person bought a cycle and sold it at a loss of 10%. If he had bought...
Suppose the cost price is Rs. x, then the selling price = 0.9x
If he had bought it for 20% less and sold it for Rs. 55 more, he would have had a profit of 40%
⇒ 0.8x × 1.4 = 0.9x + 55
⇒ 0.22x = 55
⇒ x = 250
⇒ 0.8x × 1.4 = 0.9x + 55
⇒ 0.22x = 55
⇒ x = 250
∴ Profit percentage if he sold the cycle at Rs. 320 = [320 - 250] /250 = 28%
Most Upvoted Answer
A person bought a cycle and sold it at a loss of 10%. If he had bought...
Let's assume the cost price of the cycle is C.
The person sold the cycle at a loss of 10%, which means he sold it for 90% of its cost price. Therefore, the selling price of the cycle is 0.9C.
According to the second scenario, if the person had bought the cycle for 20% less, the cost price would be 0.8C. And if he had sold it for Rs. 55 more, the selling price would be 0.9C + 55.
We also know that in this second scenario, the person would have made a profit of 40%. Therefore, the selling price in this case is 1.4 times the cost price, which can be expressed as 1.4(0.8C) = 1.12C.
Now we can equate the two selling prices:
0.9C = 1.12C + 55
Simplifying this equation, we get:
0.22C = 55
C = 55/0.22
C ≈ 250
So, the cost price of the cycle is approximately Rs. 250.
To find the profit percentage when the cycle is sold for Rs. 320, we need to calculate the profit first.
Profit = Selling Price - Cost Price
Profit = 320 - 250
Profit = 70
Now we can calculate the profit percentage:
Profit Percentage = (Profit/Cost Price) * 100
Profit Percentage = (70/250) * 100
Profit Percentage = 28%
Therefore, the profit percentage when the cycle is sold for Rs. 320 is 28%, which is option B.
The person sold the cycle at a loss of 10%, which means he sold it for 90% of its cost price. Therefore, the selling price of the cycle is 0.9C.
According to the second scenario, if the person had bought the cycle for 20% less, the cost price would be 0.8C. And if he had sold it for Rs. 55 more, the selling price would be 0.9C + 55.
We also know that in this second scenario, the person would have made a profit of 40%. Therefore, the selling price in this case is 1.4 times the cost price, which can be expressed as 1.4(0.8C) = 1.12C.
Now we can equate the two selling prices:
0.9C = 1.12C + 55
Simplifying this equation, we get:
0.22C = 55
C = 55/0.22
C ≈ 250
So, the cost price of the cycle is approximately Rs. 250.
To find the profit percentage when the cycle is sold for Rs. 320, we need to calculate the profit first.
Profit = Selling Price - Cost Price
Profit = 320 - 250
Profit = 70
Now we can calculate the profit percentage:
Profit Percentage = (Profit/Cost Price) * 100
Profit Percentage = (70/250) * 100
Profit Percentage = 28%
Therefore, the profit percentage when the cycle is sold for Rs. 320 is 28%, which is option B.
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