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How many numbers arc there between 99 and 1000 such that the digit 8 occupies the units place?
- a)64
- b)80
- c)90
- d)104
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
How many numbers arc there between 99 and 1000 such that the digit 8 o...
Numbers are: 108, 118, 128, 138, .............,998
Total = 10 x 9 =90
Total = 10 x 9 =90
Most Upvoted Answer
How many numbers arc there between 99 and 1000 such that the digit 8 o...
To find the number of numbers between 99 and 1000 such that the digit 8 occupies the units place, we can break down the problem into smaller cases and then add up the results.
Numbers in the form of XY8:
- For the hundreds place (X), we have 9 options (1-9).
- For the tens place (Y), we have 10 options (0-9).
- For the units place (8), we have only 1 option.
So, for numbers in the form of XY8, we have a total of 9 * 10 * 1 = 90 options.
Numbers in the form of X88:
- For the hundreds place (X), we have 9 options (1-9).
- For the tens place (8), we have only 1 option.
- For the units place (8), we have only 1 option.
So, for numbers in the form of X88, we have a total of 9 * 1 * 1 = 9 options.
Numbers in the form of 88Y:
- For the hundreds place (8), we have only 1 option.
- For the tens place (8), we have only 1 option.
- For the units place (Y), we have 10 options (0-9).
So, for numbers in the form of 88Y, we have a total of 1 * 1 * 10 = 10 options.
Adding up the results from all three cases, we have:
90 + 9 + 10 = 109
However, we need to exclude the number 888 as it falls outside the range between 99 and 1000. Therefore, we subtract 1 from the total.
109 - 1 = 108
Therefore, the correct answer is option C) 108.
Numbers in the form of XY8:
- For the hundreds place (X), we have 9 options (1-9).
- For the tens place (Y), we have 10 options (0-9).
- For the units place (8), we have only 1 option.
So, for numbers in the form of XY8, we have a total of 9 * 10 * 1 = 90 options.
Numbers in the form of X88:
- For the hundreds place (X), we have 9 options (1-9).
- For the tens place (8), we have only 1 option.
- For the units place (8), we have only 1 option.
So, for numbers in the form of X88, we have a total of 9 * 1 * 1 = 9 options.
Numbers in the form of 88Y:
- For the hundreds place (8), we have only 1 option.
- For the tens place (8), we have only 1 option.
- For the units place (Y), we have 10 options (0-9).
So, for numbers in the form of 88Y, we have a total of 1 * 1 * 10 = 10 options.
Adding up the results from all three cases, we have:
90 + 9 + 10 = 109
However, we need to exclude the number 888 as it falls outside the range between 99 and 1000. Therefore, we subtract 1 from the total.
109 - 1 = 108
Therefore, the correct answer is option C) 108.
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How many numbers arc there between 99 and 1000 such that the digit 8 occupies the units place?a)64b)80c)90d)104Correct answer is option 'C'. Can you explain this answer? for UPSC 2026 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about How many numbers arc there between 99 and 1000 such that the digit 8 occupies the units place?a)64b)80c)90d)104Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many numbers arc there between 99 and 1000 such that the digit 8 occupies the units place?a)64b)80c)90d)104Correct answer is option 'C'. Can you explain this answer?.
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