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A shopkeeper, who sells only apples, oranges and coconuts, is offering a strange scheme to his customers. The scheme is as follows:
If the customer buys at least one item each of the three types of fruits, the price to be paid for all the fruits of that type combined is inversely proportional to the number of fruits of that kind purchased and is directly proportional to the total number of fruits purchased. The constant of proportionality in this deal is 50.
Ajay, who is an intelligent customer, wishes to buy at least one fruit of each kind. What is the minimum price he has to pay for such a purchase?
- a)450
- b)9
- c)50
- d)150
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A shopkeeper, who sells only apples, oranges and coconuts, is offering...
Suppose Ajay purchases x apples, y oranges and z coconuts.
We know that the Harmonic Mean of any set of numbers is less than their Arithmetic Mean.
Hence, option 1.
Most Upvoted Answer
A shopkeeper, who sells only apples, oranges and coconuts, is offering...
To solve this problem, we need to understand the given scheme and calculate the minimum price Ajay has to pay for buying at least one fruit of each kind.
Given Information:
- The price to be paid for each type of fruit is inversely proportional to the number of fruits of that kind purchased.
- The price is directly proportional to the total number of fruits purchased.
- The constant of proportionality is 50.
Understanding the Scheme:
Let's assume the prices of apples, oranges, and coconuts are A, O, and C respectively. According to the scheme, the price to be paid for each type of fruit is inversely proportional to the number of fruits of that kind purchased. This means that the more fruits of a particular kind Ajay buys, the less he has to pay for each fruit of that kind.
Calculation:
Let's assume Ajay buys x apples, y oranges, and z coconuts.
According to the scheme, the price to be paid for all the apples combined is inversely proportional to the number of apples purchased and directly proportional to the total number of fruits purchased. So, the price for apples would be (50 * x)/(x + y + z).
Similarly, the price for oranges would be (50 * y)/(x + y + z) and the price for coconuts would be (50 * z)/(x + y + z).
As Ajay wants to buy at least one fruit of each kind, x, y, and z should be greater than or equal to 1.
To calculate the minimum price Ajay has to pay, we need to find the minimum value of the sum of these three prices.
Minimum Price Calculation:
To minimize the price, we need to maximize the denominators (x + y + z) for each price term.
So, we can assume x = y = z = 1 to get the minimum price.
Plugging in these values, we get:
Price for apples = (50 * 1)/(1 + 1 + 1) = 50/3
Price for oranges = (50 * 1)/(1 + 1 + 1) = 50/3
Price for coconuts = (50 * 1)/(1 + 1 + 1) = 50/3
Adding these prices, we get the minimum price Ajay has to pay:
Minimum price = (50/3) + (50/3) + (50/3) = 150/3 = 50
Therefore, the minimum price Ajay has to pay for buying at least one fruit of each kind is 50.
Hence, the correct answer is option C) 50.
Given Information:
- The price to be paid for each type of fruit is inversely proportional to the number of fruits of that kind purchased.
- The price is directly proportional to the total number of fruits purchased.
- The constant of proportionality is 50.
Understanding the Scheme:
Let's assume the prices of apples, oranges, and coconuts are A, O, and C respectively. According to the scheme, the price to be paid for each type of fruit is inversely proportional to the number of fruits of that kind purchased. This means that the more fruits of a particular kind Ajay buys, the less he has to pay for each fruit of that kind.
Calculation:
Let's assume Ajay buys x apples, y oranges, and z coconuts.
According to the scheme, the price to be paid for all the apples combined is inversely proportional to the number of apples purchased and directly proportional to the total number of fruits purchased. So, the price for apples would be (50 * x)/(x + y + z).
Similarly, the price for oranges would be (50 * y)/(x + y + z) and the price for coconuts would be (50 * z)/(x + y + z).
As Ajay wants to buy at least one fruit of each kind, x, y, and z should be greater than or equal to 1.
To calculate the minimum price Ajay has to pay, we need to find the minimum value of the sum of these three prices.
Minimum Price Calculation:
To minimize the price, we need to maximize the denominators (x + y + z) for each price term.
So, we can assume x = y = z = 1 to get the minimum price.
Plugging in these values, we get:
Price for apples = (50 * 1)/(1 + 1 + 1) = 50/3
Price for oranges = (50 * 1)/(1 + 1 + 1) = 50/3
Price for coconuts = (50 * 1)/(1 + 1 + 1) = 50/3
Adding these prices, we get the minimum price Ajay has to pay:
Minimum price = (50/3) + (50/3) + (50/3) = 150/3 = 50
Therefore, the minimum price Ajay has to pay for buying at least one fruit of each kind is 50.
Hence, the correct answer is option C) 50.
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A shopkeeper, who sells only apples, oranges and coconuts, is offering a strange scheme to his customers. The scheme is as follows:If the customer buys at least one item each of the three types of fruits, the price to be paid for all the fruits of that type combined is inversely proportional to the number of fruits of that kind purchased and is directly proportional to the total number of fruits purchased. The constant of proportionality in this deal is 50.Ajay, who is an intelligent customer, wishes to buy at least one fruit of each kind. What is the minimum price he has to pay for such a purchase?a)450b)9c)50d)150Correct answer is option 'A'. Can you explain this answer?
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A shopkeeper, who sells only apples, oranges and coconuts, is offering a strange scheme to his customers. The scheme is as follows:If the customer buys at least one item each of the three types of fruits, the price to be paid for all the fruits of that type combined is inversely proportional to the number of fruits of that kind purchased and is directly proportional to the total number of fruits purchased. The constant of proportionality in this deal is 50.Ajay, who is an intelligent customer, wishes to buy at least one fruit of each kind. What is the minimum price he has to pay for such a purchase?a)450b)9c)50d)150Correct answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shopkeeper, who sells only apples, oranges and coconuts, is offering a strange scheme to his customers. The scheme is as follows:If the customer buys at least one item each of the three types of fruits, the price to be paid for all the fruits of that type combined is inversely proportional to the number of fruits of that kind purchased and is directly proportional to the total number of fruits purchased. The constant of proportionality in this deal is 50.Ajay, who is an intelligent customer, wishes to buy at least one fruit of each kind. What is the minimum price he has to pay for such a purchase?a)450b)9c)50d)150Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper, who sells only apples, oranges and coconuts, is offering a strange scheme to his customers. The scheme is as follows:If the customer buys at least one item each of the three types of fruits, the price to be paid for all the fruits of that type combined is inversely proportional to the number of fruits of that kind purchased and is directly proportional to the total number of fruits purchased. The constant of proportionality in this deal is 50.Ajay, who is an intelligent customer, wishes to buy at least one fruit of each kind. What is the minimum price he has to pay for such a purchase?a)450b)9c)50d)150Correct answer is option 'A'. Can you explain this answer?.
A shopkeeper, who sells only apples, oranges and coconuts, is offering a strange scheme to his customers. The scheme is as follows:If the customer buys at least one item each of the three types of fruits, the price to be paid for all the fruits of that type combined is inversely proportional to the number of fruits of that kind purchased and is directly proportional to the total number of fruits purchased. The constant of proportionality in this deal is 50.Ajay, who is an intelligent customer, wishes to buy at least one fruit of each kind. What is the minimum price he has to pay for such a purchase?a)450b)9c)50d)150Correct answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shopkeeper, who sells only apples, oranges and coconuts, is offering a strange scheme to his customers. The scheme is as follows:If the customer buys at least one item each of the three types of fruits, the price to be paid for all the fruits of that type combined is inversely proportional to the number of fruits of that kind purchased and is directly proportional to the total number of fruits purchased. The constant of proportionality in this deal is 50.Ajay, who is an intelligent customer, wishes to buy at least one fruit of each kind. What is the minimum price he has to pay for such a purchase?a)450b)9c)50d)150Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper, who sells only apples, oranges and coconuts, is offering a strange scheme to his customers. The scheme is as follows:If the customer buys at least one item each of the three types of fruits, the price to be paid for all the fruits of that type combined is inversely proportional to the number of fruits of that kind purchased and is directly proportional to the total number of fruits purchased. The constant of proportionality in this deal is 50.Ajay, who is an intelligent customer, wishes to buy at least one fruit of each kind. What is the minimum price he has to pay for such a purchase?a)450b)9c)50d)150Correct answer is option 'A'. Can you explain this answer?.
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ample number of questions to practice A shopkeeper, who sells only apples, oranges and coconuts, is offering a strange scheme to his customers. The scheme is as follows:If the customer buys at least one item each of the three types of fruits, the price to be paid for all the fruits of that type combined is inversely proportional to the number of fruits of that kind purchased and is directly proportional to the total number of fruits purchased. The constant of proportionality in this deal is 50.Ajay, who is an intelligent customer, wishes to buy at least one fruit of each kind. What is the minimum price he has to pay for such a purchase?a)450b)9c)50d)150Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
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