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An item was bought at Rs. X and sold at Rs.Y, thereby earning a profit of 20%. Had the value of X been 15% less and the value of Y been Rs.60 less, a profit of 20% would have been earned, What was the value of Y ?
- a)350
- b)400
- c)450
- d)500
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
An item was bought at Rs. X and sold at Rs.Y, thereby 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 had been Rs.60 less, a profit of 20% would have been earned.
To find:
The value of Y.
Solution:
Let's assume the cost price (X) is C and the selling price (Y) is S.
First scenario:
- Profit earned = Selling price - Cost price = S - C
- Profit percentage = (Profit/Cost price) x 100 = (S - C)/C x 100
Given that the profit percentage is 20%, we can write the equation as:
(S - C)/C x 100 = 20
S - C = 0.2C
S = 1.2C
Second scenario:
- In this scenario, the value of X is 15% less than C, so the new cost price becomes 0.85C.
- The value of Y is Rs.60 less than S, so the new selling price becomes S - 60.
- Profit earned = New selling price - New cost price = (S - 60) - 0.85C
- Profit percentage = (Profit/New cost price) x 100 = [(S - 60) - 0.85C]/0.85C x 100
Given that the profit percentage is 20%, we can write the equation as:
[(S - 60) - 0.85C]/0.85C x 100 = 20
(S - 60) - 0.85C = 0.2(0.85C)
S - 60 - 0.85C = 0.17C
S = 0.17C + 0.85C + 60
S = 1.02C + 60
Since the value of Y remains the same in both scenarios, we can equate the two expressions for S:
1.2C = 1.02C + 60
0.18C = 60
C = 60/0.18
C = 333.33 (approx)
Now, substituting the value of C in the first scenario equation to find S:
S = 1.2C
S = 1.2 x 333.33
S = 400
Hence, the value of Y is 400.
Therefore, the correct answer is option B) 400.
- 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 had been Rs.60 less, a profit of 20% would have been earned.
To find:
The value of Y.
Solution:
Let's assume the cost price (X) is C and the selling price (Y) is S.
First scenario:
- Profit earned = Selling price - Cost price = S - C
- Profit percentage = (Profit/Cost price) x 100 = (S - C)/C x 100
Given that the profit percentage is 20%, we can write the equation as:
(S - C)/C x 100 = 20
S - C = 0.2C
S = 1.2C
Second scenario:
- In this scenario, the value of X is 15% less than C, so the new cost price becomes 0.85C.
- The value of Y is Rs.60 less than S, so the new selling price becomes S - 60.
- Profit earned = New selling price - New cost price = (S - 60) - 0.85C
- Profit percentage = (Profit/New cost price) x 100 = [(S - 60) - 0.85C]/0.85C x 100
Given that the profit percentage is 20%, we can write the equation as:
[(S - 60) - 0.85C]/0.85C x 100 = 20
(S - 60) - 0.85C = 0.2(0.85C)
S - 60 - 0.85C = 0.17C
S = 0.17C + 0.85C + 60
S = 1.02C + 60
Since the value of Y remains the same in both scenarios, we can equate the two expressions for S:
1.2C = 1.02C + 60
0.18C = 60
C = 60/0.18
C = 333.33 (approx)
Now, substituting the value of C in the first scenario equation to find S:
S = 1.2C
S = 1.2 x 333.33
S = 400
Hence, the value of Y is 400.
Therefore, the correct answer is option B) 400.
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Community Answer
An item was bought at Rs. X and sold at Rs.Y, thereby earning a profit...
x(1.2)=y———–1
x(0.85)(1.2)=y-60——————-2
Sub 1 in 2, and solve y
Y=400
x(0.85)(1.2)=y-60——————-2
Sub 1 in 2, and solve y
Y=400
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