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There are certain 2-digit numbers. The difference between the number and the one obtained on reversing it is always 27. How many such maximum 2-digit numbers are there?
- a)3
- b)4
- c)5
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
There are certain 2-digit numbers. The difference between the number a...
Required numbers = (14, 41), (25, 52), (36, 63), (47, 74), (58, 85), (69, 96)
OR,
Let number = 10x + y
Obtain number after reversing = 10y + x
Now,
(10x + y) – (10y + x) = 27
⇒ 9x – 9y = 27
⇒ x – y = 3
Now we can put, y = 1, 2, 3, 4, 5
and 6 and x = 4, 5, 6, 7, 8 and 9
On doing this, we got more than five numbers. Hence, the correct option is (d).
OR,
Let number = 10x + y
Obtain number after reversing = 10y + x
Now,
(10x + y) – (10y + x) = 27
⇒ 9x – 9y = 27
⇒ x – y = 3
Now we can put, y = 1, 2, 3, 4, 5
and 6 and x = 4, 5, 6, 7, 8 and 9
On doing this, we got more than five numbers. Hence, the correct option is (d).
Most Upvoted Answer
There are certain 2-digit numbers. The difference between the number a...
Solution:
Let the number be xy, where x and y are digits.
The number can be written as 10x+y, and the reversed number can be written as 10y+x.
The difference between the two numbers is:
(10x+y)-(10y+x) = 9x-9y = 9(x-y)
Given that the difference is 27, we have:
9(x-y) = 27
Simplifying, we get:
x-y = 3
This means that the digits differ by 3.
We need to find maximum 2-digit numbers that satisfy this condition.
Let us list all such numbers:
- 12 (21)
- 23 (32)
- 34 (43)
- 45 (54)
- 56 (65)
- 67 (76)
- 78 (87)
- 89 (98)
Thus, there are no such maximum 2-digit numbers that satisfy the condition. Hence, the correct answer is option D.
Let the number be xy, where x and y are digits.
The number can be written as 10x+y, and the reversed number can be written as 10y+x.
The difference between the two numbers is:
(10x+y)-(10y+x) = 9x-9y = 9(x-y)
Given that the difference is 27, we have:
9(x-y) = 27
Simplifying, we get:
x-y = 3
This means that the digits differ by 3.
We need to find maximum 2-digit numbers that satisfy this condition.
Let us list all such numbers:
- 12 (21)
- 23 (32)
- 34 (43)
- 45 (54)
- 56 (65)
- 67 (76)
- 78 (87)
- 89 (98)
Thus, there are no such maximum 2-digit numbers that satisfy the condition. Hence, the correct answer is option D.
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There are certain 2-digit numbers. The difference between the number and the one obtained on reversing it is always 27. How many such maximum 2-digit numbers are there?a)3b)4c)5d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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