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A vendor has two types of grapes. One is the fresh grapes containing 80% water and dry grapes containing 25% water. He sells 20 kg dry grapes, by adding water to the dry grapes, at cost price. What is the total profit percentage when after adding water the weight of 20 kg dry grapes increase in the proportion of water in fresh grapes?
- a)265%
- b)200%
- c)280%
- d)275%
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A vendor has two types of grapes. One is the fresh grapes containing 8...
Fresh grapes
Water: Pulp = 80% : 20% = 4 : 1
Dry grapes
Water: Pulp = 25% : 75% = 1 : 3
So out of 20 kg dry grapes, Water : Pulp = 5 kg : 15 kg
After adding of water the ratio of water : pulp is same as the fresh grapes = 4 : 1
After adding water the quantity of Water and Pulp are 60 kg and 15 kg respectively.
% = 55/20 * 100 = 275%
Water: Pulp = 80% : 20% = 4 : 1
Dry grapes
Water: Pulp = 25% : 75% = 1 : 3
So out of 20 kg dry grapes, Water : Pulp = 5 kg : 15 kg
After adding of water the ratio of water : pulp is same as the fresh grapes = 4 : 1
After adding water the quantity of Water and Pulp are 60 kg and 15 kg respectively.
% = 55/20 * 100 = 275%
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A vendor has two types of grapes. One is the fresh grapes containing 8...
Given:
- Fresh grapes contain 80% water
- Dry grapes contain 25% water
- 20 kg dry grapes are sold by adding water to them
- The weight of 20 kg dry grapes increases in the proportion of water in fresh grapes
To find:
- Total profit percentage
Solution:
Let's assume that x kg of water is added to 20 kg of dry grapes to make them fresh.
So, the weight of the fresh grapes = 20 + x kg
Also, we know that the weight of water in fresh grapes and dry grapes is the same.
Weight of water in fresh grapes = 80% of (20 + x) kg
Weight of water in dry grapes = 25% of 20 kg
So, we can write:
0.8(20 + x) = 0.25(20)
16 + 0.8x = 5
0.8x = -11
x = -11/0.8
x = -13.75 kg (Negative value means water needs to be removed)
This means that 13.75 kg of water needs to be removed from 20 kg dry grapes to get fresh grapes.
So, the weight of fresh grapes = 20 - 13.75 = 6.25 kg
And, the cost price of 20 kg dry grapes = cost price of 6.25 kg fresh grapes (since water is added at cost price)
Let's assume the cost price of 1 kg of dry grapes = Rs. x
Then, the cost price of 1 kg of fresh grapes = cost price of (1 - 0.8) kg of dry grapes (since 80% of fresh grapes is water)
= cost price of 0.2 kg of dry grapes
= 0.2x
Cost price of 6.25 kg of fresh grapes = 6.25 * 0.2x
= 1.25x
Now, let's assume that the vendor sells the 20 kg of fresh grapes at Rs. y per kg.
So, the total selling price of 20 kg of fresh grapes = 20 * y
Profit = Selling price - Cost price
= (20 * y) - (1.25x)
Profit percentage = (Profit / Cost price) * 100
= [(20 * y) - (1.25x)] / (1.25x) * 100
We need to find the value of y that maximizes the profit percentage.
Let's differentiate the profit percentage expression w.r.t y and equate it to zero to find the maximum value.
d/dy [(20 * y) - (1.25x)] / (1.25x) = 0
20 / (1.25x) = 0
y = (1.25x * 0.2) = 0.25x
So, the maximum profit percentage is obtained when the selling price of fresh grapes is 0.25 times the cost price of dry grapes.
Let's substitute this value of y in the profit percentage expression.
Profit percentage = [(20 * 0.25x) - (1.25x)] / (1.25x) * 100
= (2.5x - 1.25x) / 1.25x * 100
= 100%
But
- Fresh grapes contain 80% water
- Dry grapes contain 25% water
- 20 kg dry grapes are sold by adding water to them
- The weight of 20 kg dry grapes increases in the proportion of water in fresh grapes
To find:
- Total profit percentage
Solution:
Let's assume that x kg of water is added to 20 kg of dry grapes to make them fresh.
So, the weight of the fresh grapes = 20 + x kg
Also, we know that the weight of water in fresh grapes and dry grapes is the same.
Weight of water in fresh grapes = 80% of (20 + x) kg
Weight of water in dry grapes = 25% of 20 kg
So, we can write:
0.8(20 + x) = 0.25(20)
16 + 0.8x = 5
0.8x = -11
x = -11/0.8
x = -13.75 kg (Negative value means water needs to be removed)
This means that 13.75 kg of water needs to be removed from 20 kg dry grapes to get fresh grapes.
So, the weight of fresh grapes = 20 - 13.75 = 6.25 kg
And, the cost price of 20 kg dry grapes = cost price of 6.25 kg fresh grapes (since water is added at cost price)
Let's assume the cost price of 1 kg of dry grapes = Rs. x
Then, the cost price of 1 kg of fresh grapes = cost price of (1 - 0.8) kg of dry grapes (since 80% of fresh grapes is water)
= cost price of 0.2 kg of dry grapes
= 0.2x
Cost price of 6.25 kg of fresh grapes = 6.25 * 0.2x
= 1.25x
Now, let's assume that the vendor sells the 20 kg of fresh grapes at Rs. y per kg.
So, the total selling price of 20 kg of fresh grapes = 20 * y
Profit = Selling price - Cost price
= (20 * y) - (1.25x)
Profit percentage = (Profit / Cost price) * 100
= [(20 * y) - (1.25x)] / (1.25x) * 100
We need to find the value of y that maximizes the profit percentage.
Let's differentiate the profit percentage expression w.r.t y and equate it to zero to find the maximum value.
d/dy [(20 * y) - (1.25x)] / (1.25x) = 0
20 / (1.25x) = 0
y = (1.25x * 0.2) = 0.25x
So, the maximum profit percentage is obtained when the selling price of fresh grapes is 0.25 times the cost price of dry grapes.
Let's substitute this value of y in the profit percentage expression.
Profit percentage = [(20 * 0.25x) - (1.25x)] / (1.25x) * 100
= (2.5x - 1.25x) / 1.25x * 100
= 100%
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A vendor has two types of grapes. One is the fresh grapes containing 80% water and dry grapes containing 25% water. He sells 20 kg dry grapes, by adding water to the dry grapes, at cost price. What is the total profit percentage when after adding water the weight of 20 kg dry grapes increase in the proportion of water in fresh grapes?a)265%b)200%c)280%d)275%e)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A vendor has two types of grapes. One is the fresh grapes containing 80% water and dry grapes containing 25% water. He sells 20 kg dry grapes, by adding water to the dry grapes, at cost price. What is the total profit percentage when after adding water the weight of 20 kg dry grapes increase in the proportion of water in fresh grapes?a)265%b)200%c)280%d)275%e)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vendor has two types of grapes. One is the fresh grapes containing 80% water and dry grapes containing 25% water. He sells 20 kg dry grapes, by adding water to the dry grapes, at cost price. What is the total profit percentage when after adding water the weight of 20 kg dry grapes increase in the proportion of water in fresh grapes?a)265%b)200%c)280%d)275%e)None of theseCorrect answer is option 'D'. Can you explain this answer?.
A vendor has two types of grapes. One is the fresh grapes containing 80% water and dry grapes containing 25% water. He sells 20 kg dry grapes, by adding water to the dry grapes, at cost price. What is the total profit percentage when after adding water the weight of 20 kg dry grapes increase in the proportion of water in fresh grapes?a)265%b)200%c)280%d)275%e)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A vendor has two types of grapes. One is the fresh grapes containing 80% water and dry grapes containing 25% water. He sells 20 kg dry grapes, by adding water to the dry grapes, at cost price. What is the total profit percentage when after adding water the weight of 20 kg dry grapes increase in the proportion of water in fresh grapes?a)265%b)200%c)280%d)275%e)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vendor has two types of grapes. One is the fresh grapes containing 80% water and dry grapes containing 25% water. He sells 20 kg dry grapes, by adding water to the dry grapes, at cost price. What is the total profit percentage when after adding water the weight of 20 kg dry grapes increase in the proportion of water in fresh grapes?a)265%b)200%c)280%d)275%e)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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