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An item was bought at Rs x and sold at Rs y, there by earning a profit of 20%. Had the value of x been 15% less and the value of y Rs 76 less, a profit of 30% would have been earned. What was the value of x.
- a)Rs 640
- b)Rs 400
- c)Rs 600
- d)Rs 800
- e)Rs 840
Correct answer is option 'D'. Can you explain this answer?
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An item was bought at Rs x and sold at Rs y, there by earning a profit...
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An item was bought at Rs x and sold at Rs y, there by earning a profit...
Given:
- An item was bought at Rs x and sold at Rs y, thereby earning a profit of 20%.
- If the value of x had been 15% less and the value of y Rs 76 less, a profit of 30% would have been earned.
To find:
The value of x.
Assumptions:
Let's assume the cost price (CP) of the item is P.
Solution:
Step 1: Finding the equation:
According to the given information, we can form the following equation:
Profit% = [(Selling Price - Cost Price) / Cost Price] * 100
For the first scenario, where a profit of 20% is earned:
20 = [(y - x) / x] * 100
20 = (y - x) * 100 / x
20x = 100y - 100x
120x = 100y
For the second scenario, where a profit of 30% would have been earned if the value of x had been 15% less and the value of y Rs 76 less:
30 = [(y - 76 - 0.85x) / 0.85x] * 100
30 = (y - 76 - 0.85x) * 100 / 0.85x
30 * 0.85x = 100y - 76
25.5x = 100y - 76
Step 2: Solving the equations:
Now, we have two equations:
120x = 100y
25.5x = 100y - 76
Solving these equations will give us the value of x.
Dividing the second equation by 25.5, we get:
x = (100y - 76) / 25.5
Substituting the value of x in the first equation, we have:
120[(100y - 76) / 25.5] = 100y
(120 * 100y - 120 * 76) / 25.5 = 100y
(12000y - 9120) / 25.5 = 100y
12000y - 9120 = 2550y
12000y - 2550y = 9120
9450y = 9120
y = 9120 / 9450
y = 0.96
Step 3: Finding the value of x:
Substituting the value of y in the second equation, we have:
x = (100 * 0.96 - 76) / 25.5
x = 96 - 76 / 25.5
x = 20 / 25.5
x = 0.784
Since the given options are in the form of Rs, we need to multiply the value of x by 100 to convert it into Rs.
x = 0.784 * 100
x = 78.4
Therefore, the value of x is Rs 78.4, which is not among the given options.
Conclusion:
The given answer, option 'D' (Rs 800), is incorrect. There might be an error in the given
- An item was bought at Rs x and sold at Rs y, thereby earning a profit of 20%.
- If the value of x had been 15% less and the value of y Rs 76 less, a profit of 30% would have been earned.
To find:
The value of x.
Assumptions:
Let's assume the cost price (CP) of the item is P.
Solution:
Step 1: Finding the equation:
According to the given information, we can form the following equation:
Profit% = [(Selling Price - Cost Price) / Cost Price] * 100
For the first scenario, where a profit of 20% is earned:
20 = [(y - x) / x] * 100
20 = (y - x) * 100 / x
20x = 100y - 100x
120x = 100y
For the second scenario, where a profit of 30% would have been earned if the value of x had been 15% less and the value of y Rs 76 less:
30 = [(y - 76 - 0.85x) / 0.85x] * 100
30 = (y - 76 - 0.85x) * 100 / 0.85x
30 * 0.85x = 100y - 76
25.5x = 100y - 76
Step 2: Solving the equations:
Now, we have two equations:
120x = 100y
25.5x = 100y - 76
Solving these equations will give us the value of x.
Dividing the second equation by 25.5, we get:
x = (100y - 76) / 25.5
Substituting the value of x in the first equation, we have:
120[(100y - 76) / 25.5] = 100y
(120 * 100y - 120 * 76) / 25.5 = 100y
(12000y - 9120) / 25.5 = 100y
12000y - 9120 = 2550y
12000y - 2550y = 9120
9450y = 9120
y = 9120 / 9450
y = 0.96
Step 3: Finding the value of x:
Substituting the value of y in the second equation, we have:
x = (100 * 0.96 - 76) / 25.5
x = 96 - 76 / 25.5
x = 20 / 25.5
x = 0.784
Since the given options are in the form of Rs, we need to multiply the value of x by 100 to convert it into Rs.
x = 0.784 * 100
x = 78.4
Therefore, the value of x is Rs 78.4, which is not among the given options.
Conclusion:
The given answer, option 'D' (Rs 800), is incorrect. There might be an error in the given
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An item was bought at Rs x and sold at Rs y, there by earning a profit of 20%. Had the value of x been 15% less and the value of y Rs 76 less, a profit of 30% would have been earned. What was the value of x.a)Rs 640b)Rs 400c)Rs 600d)Rs 800e)Rs 840Correct answer is option 'D'. Can you explain this answer?
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