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A shopkeeper sold an article at a profit of 20%. If he had bought it at 20% less and sold it for Rs. 75 less, he would have earned a profit of 25%. Find the cost price of the article.
- a)Rs. 420
- b)Rs. 355
- c)Rs. 375
- d)Rs. 320
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A shopkeeper sold an article at a profit of 20%. If he had bought it ...
Problem: To find the cost price of an article.
Given:
Profit = 20%
If bought at 20% less and sold for Rs. 75 less, profit = 25%
Let's assume the cost price of the article is x.
Solution:
Case 1: When the profit is 20%.
Selling price = cost price + profit
SP = x + 20% of x
SP = x + 0.2x
SP = 1.2x
Case 2: When the profit is 25%.
Let's find the cost price of the article when bought at 20% less i.e., 0.8x.
Selling price = cost price + profit
SP = 0.8x + 25% of 0.8x - Rs. 75
SP = 0.8x + 0.2x - 75
SP = x - 75
Now, equating the selling prices from both cases, we get:
1.2x = x - 75
0.2x = -75
x = -375/2 = -187.5
The cost price cannot be negative. Therefore, there must be some mistake in our calculation. Let's check.
We assumed the cost price to be x. However, we forgot that the cost price cannot be negative. Therefore, we need to assume the cost price to be y (some positive value).
Case 1: When the profit is 20%.
Selling price = cost price + profit
SP = y + 20% of y
SP = y + 0.2y
SP = 1.2y
Case 2: When the profit is 25%.
Let's find the cost price of the article when bought at 20% less i.e., 0.8y.
Selling price = cost price + profit
SP = 0.8y + 25% of 0.8y - Rs. 75
SP = 0.8y + 0.2y - 75
SP = y - 75
Now, equating the selling prices from both cases, we get:
1.2y = y - 75
0.2y = -75
y = -375
Again, the cost price cannot be negative. Therefore, there must be some mistake in our calculation. Let's check.
We assumed the profit to be 20% and 25%. However, we forgot that the profit cannot be negative. Therefore, we need to assume the profit to be p (some positive value).
Case 1: When the profit is p%.
Selling price = cost price + profit
SP = y + p% of y
SP = y + py/100
SP = (100+p)y/100
Case 2: When the profit is (p+5)%.
Let's find the cost price of the article when bought at 20% less i.e., 0.8y.
Selling price = cost price + profit
SP = 0.8y + (p+5)% of 0.8y - Rs. 75
SP = 0.8y + (p+5)% of 0.8y - 75
SP = (100+p+5)0.8y/100 - 75
SP =
Given:
Profit = 20%
If bought at 20% less and sold for Rs. 75 less, profit = 25%
Let's assume the cost price of the article is x.
Solution:
Case 1: When the profit is 20%.
Selling price = cost price + profit
SP = x + 20% of x
SP = x + 0.2x
SP = 1.2x
Case 2: When the profit is 25%.
Let's find the cost price of the article when bought at 20% less i.e., 0.8x.
Selling price = cost price + profit
SP = 0.8x + 25% of 0.8x - Rs. 75
SP = 0.8x + 0.2x - 75
SP = x - 75
Now, equating the selling prices from both cases, we get:
1.2x = x - 75
0.2x = -75
x = -375/2 = -187.5
The cost price cannot be negative. Therefore, there must be some mistake in our calculation. Let's check.
We assumed the cost price to be x. However, we forgot that the cost price cannot be negative. Therefore, we need to assume the cost price to be y (some positive value).
Case 1: When the profit is 20%.
Selling price = cost price + profit
SP = y + 20% of y
SP = y + 0.2y
SP = 1.2y
Case 2: When the profit is 25%.
Let's find the cost price of the article when bought at 20% less i.e., 0.8y.
Selling price = cost price + profit
SP = 0.8y + 25% of 0.8y - Rs. 75
SP = 0.8y + 0.2y - 75
SP = y - 75
Now, equating the selling prices from both cases, we get:
1.2y = y - 75
0.2y = -75
y = -375
Again, the cost price cannot be negative. Therefore, there must be some mistake in our calculation. Let's check.
We assumed the profit to be 20% and 25%. However, we forgot that the profit cannot be negative. Therefore, we need to assume the profit to be p (some positive value).
Case 1: When the profit is p%.
Selling price = cost price + profit
SP = y + p% of y
SP = y + py/100
SP = (100+p)y/100
Case 2: When the profit is (p+5)%.
Let's find the cost price of the article when bought at 20% less i.e., 0.8y.
Selling price = cost price + profit
SP = 0.8y + (p+5)% of 0.8y - Rs. 75
SP = 0.8y + (p+5)% of 0.8y - 75
SP = (100+p+5)0.8y/100 - 75
SP =
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Community Answer
A shopkeeper sold an article at a profit of 20%. If he had bought it ...
Let cost price of article be Rs. 100.
Then, SP = Rs. 120
If bought at 20% less, then CP = 80.
Profit % = 25%
So, selling price of the article = (80 × 125)/100
Selling price = Rs. 100
Now, difference between both the selling prices is Rs. 20 (120 - 100), when cost price is Rs. 100.
When difference between both the selling prices is Rs. 75, then cost price would be (100 x 75)/20 = 375
Therefore, cost price of article = Rs. 375
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A shopkeeper sold an article at a profit of 20%. If he had bought it at 20% less and sold it for Rs. 75 less, he would have earned a profit of 25%. Find the cost price of the article.a)Rs. 420b)Rs. 355c)Rs. 375d)Rs. 320e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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