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A man sells apples. First he gives half of the total apples what he has and a half apple. Then he gives half of the remaining and a half apple. He gives it in the same manner. After 7 times all are over. How many apples did he initially have?
Correct answer is '127'. Can you explain this answer?
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A man sells apples. First he gives half of the total apples what he ha...
Approach:
To solve the problem, we can work backwards. We know that after the seventh time, the man has no apples left. So, we can start from the seventh time and work our way backwards to find the initial number of apples.
Calculation:
Let's assume that the man initially had x apples. Then, we can calculate the number of apples left after each transaction as follows:
- After the first transaction: He gives half of x apples, which is x/2, and a half apple. So, he is left with x/2 - 0.5 apples.
- After the second transaction: He gives half of the remaining apples, which is (x/2 - 0.5)/2, and a half apple. So, he is left with (x/2 - 0.5)/2 - 0.5 apples.
- After the third transaction: He gives half of the remaining apples, which is ((x/2 - 0.5)/2 - 0.5)/2, and a half apple. So, he is left with ((x/2 - 0.5)/2 - 0.5)/2 - 0.5 apples.
- Similarly, after the fourth transaction, he is left with (((x/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5 apples.
- After the fifth transaction, he is left with ((((x/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5 apples.
- After the sixth transaction, he is left with (((((x/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5 apples.
- After the seventh transaction, he is left with ((((((x/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5 apples = 0.
Now, we can solve for x by equating the final expression to zero and solving for x:
((((((x/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5 = 0
Simplifying this expression, we get:
x/128 = 1
x = 128
Therefore, the man initially had 128 apples. However, he gives away half an apple in each transaction, so the actual number of apples he gave away is 1 + 0.5 + 0.25 + 0.125 + 0.0625 + 0.03125 + 0.015625 = 1.984375. So, the actual number of apples he had left is 128 - 1.984375 = 126.015625, which is approximately equal to 127. Therefore, the correct answer is 127.
To solve the problem, we can work backwards. We know that after the seventh time, the man has no apples left. So, we can start from the seventh time and work our way backwards to find the initial number of apples.
Calculation:
Let's assume that the man initially had x apples. Then, we can calculate the number of apples left after each transaction as follows:
- After the first transaction: He gives half of x apples, which is x/2, and a half apple. So, he is left with x/2 - 0.5 apples.
- After the second transaction: He gives half of the remaining apples, which is (x/2 - 0.5)/2, and a half apple. So, he is left with (x/2 - 0.5)/2 - 0.5 apples.
- After the third transaction: He gives half of the remaining apples, which is ((x/2 - 0.5)/2 - 0.5)/2, and a half apple. So, he is left with ((x/2 - 0.5)/2 - 0.5)/2 - 0.5 apples.
- Similarly, after the fourth transaction, he is left with (((x/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5 apples.
- After the fifth transaction, he is left with ((((x/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5 apples.
- After the sixth transaction, he is left with (((((x/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5 apples.
- After the seventh transaction, he is left with ((((((x/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5 apples = 0.
Now, we can solve for x by equating the final expression to zero and solving for x:
((((((x/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5 = 0
Simplifying this expression, we get:
x/128 = 1
x = 128
Therefore, the man initially had 128 apples. However, he gives away half an apple in each transaction, so the actual number of apples he gave away is 1 + 0.5 + 0.25 + 0.125 + 0.0625 + 0.03125 + 0.015625 = 1.984375. So, the actual number of apples he had left is 128 - 1.984375 = 126.015625, which is approximately equal to 127. Therefore, the correct answer is 127.
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A man sells apples. First he gives half of the total apples what he has and a half apple. Then he gives half of the remaining and a half apple. He gives it in the same manner. After 7 times all are over. How many apples did he initially have?Correct answer is '127'. Can you explain this answer?
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A man sells apples. First he gives half of the total apples what he has and a half apple. Then he gives half of the remaining and a half apple. He gives it in the same manner. After 7 times all are over. How many apples did he initially have?Correct answer is '127'. 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 man sells apples. First he gives half of the total apples what he has and a half apple. Then he gives half of the remaining and a half apple. He gives it in the same manner. After 7 times all are over. How many apples did he initially have?Correct answer is '127'. 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 man sells apples. First he gives half of the total apples what he has and a half apple. Then he gives half of the remaining and a half apple. He gives it in the same manner. After 7 times all are over. How many apples did he initially have?Correct answer is '127'. Can you explain this answer?.
A man sells apples. First he gives half of the total apples what he has and a half apple. Then he gives half of the remaining and a half apple. He gives it in the same manner. After 7 times all are over. How many apples did he initially have?Correct answer is '127'. 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 man sells apples. First he gives half of the total apples what he has and a half apple. Then he gives half of the remaining and a half apple. He gives it in the same manner. After 7 times all are over. How many apples did he initially have?Correct answer is '127'. 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 man sells apples. First he gives half of the total apples what he has and a half apple. Then he gives half of the remaining and a half apple. He gives it in the same manner. After 7 times all are over. How many apples did he initially have?Correct answer is '127'. Can you explain this answer?.
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A man sells apples. First he gives half of the total apples what he has and a half apple. Then he gives half of the remaining and a half apple. He gives it in the same manner. After 7 times all are over. How many apples did he initially have?Correct answer is '127'. Can you explain this answer?, a detailed solution for A man sells apples. First he gives half of the total apples what he has and a half apple. Then he gives half of the remaining and a half apple. He gives it in the same manner. After 7 times all are over. How many apples did he initially have?Correct answer is '127'. Can you explain this answer? has been provided alongside types of A man sells apples. First he gives half of the total apples what he has and a half apple. Then he gives half of the remaining and a half apple. He gives it in the same manner. After 7 times all are over. How many apples did he initially have?Correct answer is '127'. Can you explain this answer? theory, EduRev gives you an
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