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A group of friends have some money which was in an increasing GP. The total money with the first and the last friend was Rs 66 and the product of the money that the second friend had and that the last but one friend had was Rs 128. If the total money with all of them together was Rs 126, then how many friends were there?
- a)6
- b)5
- c)3
- d)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A group of friends have some money which was in an increasing GP. The ...
The sum of money with the first and the last friend = 66. This can be used as a hint. Let us assume the first friend was having Rs 2 and the last friend was having Rs 64. So, the money can be in the sequence 2, 4, 8, 16, 32, 64. It satisfies the given conditions. Alternatively, this can be done by using the formula for tn of GP also.
Most Upvoted Answer
A group of friends have some money which was in an increasing GP. The ...
Given:
Total money with first and last friend = Rs 66
Product of money of second and second last friend = Rs 128
Total money with all friends = Rs 126
To find: Number of friends
Let the amount of money with the first friend be x. Then we can write the following:
Money with the first friend = x
Money with the last friend = 66 - x (because total money with first and last friend = Rs 66)
Product of money of second and second last friend = 128
Money with the second last friend = y (let's assume)
Money with the second friend = 128/y (because product of their money is 128)
Now, let's try to write an equation for the total money with all the friends:
x + 128/y + y + 66 - x = 126
Simplifying this equation, we get:
128/y + y = 60
Multiplying both sides by y, we get:
128 + y^2 = 60y
Rearranging and simplifying, we get:
y^2 - 60y + 128 = 0
Solving this quadratic equation using the quadratic formula, we get:
y = 8 or y = 52
If y = 8, then the money with the second friend is 16 and the money with the second last friend is 8. But in this case, the money with the first friend would be negative, which is not possible.
If y = 52, then the money with the second friend is 128/52 = 2.46 (approx) and the money with the second last friend is 52. Then the money with the first friend is 12 and the money with the last friend is 54.
Hence, there are 6 friends in total.
Therefore, the correct answer is option A.
Total money with first and last friend = Rs 66
Product of money of second and second last friend = Rs 128
Total money with all friends = Rs 126
To find: Number of friends
Let the amount of money with the first friend be x. Then we can write the following:
Money with the first friend = x
Money with the last friend = 66 - x (because total money with first and last friend = Rs 66)
Product of money of second and second last friend = 128
Money with the second last friend = y (let's assume)
Money with the second friend = 128/y (because product of their money is 128)
Now, let's try to write an equation for the total money with all the friends:
x + 128/y + y + 66 - x = 126
Simplifying this equation, we get:
128/y + y = 60
Multiplying both sides by y, we get:
128 + y^2 = 60y
Rearranging and simplifying, we get:
y^2 - 60y + 128 = 0
Solving this quadratic equation using the quadratic formula, we get:
y = 8 or y = 52
If y = 8, then the money with the second friend is 16 and the money with the second last friend is 8. But in this case, the money with the first friend would be negative, which is not possible.
If y = 52, then the money with the second friend is 128/52 = 2.46 (approx) and the money with the second last friend is 52. Then the money with the first friend is 12 and the money with the last friend is 54.
Hence, there are 6 friends in total.
Therefore, the correct answer is option A.
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A group of friends have some money which was in an increasing GP. The total money with the first and the last friend was Rs 66 and the product of the money that the second friend had and that the last but one friend had was Rs 128. If the total money with all of them together was Rs 126, then how many friends were there?a)6b)5c)3d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?
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A group of friends have some money which was in an increasing GP. The total money with the first and the last friend was Rs 66 and the product of the money that the second friend had and that the last but one friend had was Rs 128. If the total money with all of them together was Rs 126, then how many friends were there?a)6b)5c)3d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A group of friends have some money which was in an increasing GP. The total money with the first and the last friend was Rs 66 and the product of the money that the second friend had and that the last but one friend had was Rs 128. If the total money with all of them together was Rs 126, then how many friends were there?a)6b)5c)3d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A group of friends have some money which was in an increasing GP. The total money with the first and the last friend was Rs 66 and the product of the money that the second friend had and that the last but one friend had was Rs 128. If the total money with all of them together was Rs 126, then how many friends were there?a)6b)5c)3d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
A group of friends have some money which was in an increasing GP. The total money with the first and the last friend was Rs 66 and the product of the money that the second friend had and that the last but one friend had was Rs 128. If the total money with all of them together was Rs 126, then how many friends were there?a)6b)5c)3d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A group of friends have some money which was in an increasing GP. The total money with the first and the last friend was Rs 66 and the product of the money that the second friend had and that the last but one friend had was Rs 128. If the total money with all of them together was Rs 126, then how many friends were there?a)6b)5c)3d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A group of friends have some money which was in an increasing GP. The total money with the first and the last friend was Rs 66 and the product of the money that the second friend had and that the last but one friend had was Rs 128. If the total money with all of them together was Rs 126, then how many friends were there?a)6b)5c)3d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
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