Let the two digits of the number be 'a' and 'b', where 'a' is the tens digit and 'b' is the units digit.
According to the problem, the sum of the two digits number and the number obtained by reversing the digits is 66.
This can be expressed mathematically as:
10a + b + 10b + a = 66
Simplifying the above equation, we get:
11a + 11b = 66
a + b = 6
We also know that the digits differ by 2. Therefore, we can write:
a - b = 2
Solving the above two equations simultaneously, we get:
a = 4 and b = 2
Therefore, the two-digit number is 42.
Correct Question :
Q. The sum of a two digit number and the number obtained by reversing the digits is 66. If the digit of the number differ by 2, find the number
Answer:
The two digits are 42 and 24
Step by step explaination :
Let the two digit be x and y
∴ Number (2−digit) =10×x+y
Sum of 2 - digit and reverse of it
⟹10x+y+10y+x=66 (given)
∴x+y=6 (equation 1)
Digits differ by 2
∴x−y=2 (equation 2)
On adding,
2x=8
⟹x=4
∴y=2
or, x+y=6 From 1 equation
and y−x=2 From 2 equation
On adding:
2y=8
y=4
x=2
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Answers & Comments
Let the two digits of the number be 'a' and 'b', where 'a' is the tens digit and 'b' is the units digit.
According to the problem, the sum of the two digits number and the number obtained by reversing the digits is 66.
This can be expressed mathematically as:
10a + b + 10b + a = 66
Simplifying the above equation, we get:
11a + 11b = 66
a + b = 6
We also know that the digits differ by 2. Therefore, we can write:
a - b = 2
Solving the above two equations simultaneously, we get:
a = 4 and b = 2
Therefore, the two-digit number is 42.
Verified answer
Correct Question :
Q. The sum of a two digit number and the number obtained by reversing the digits is 66. If the digit of the number differ by 2, find the number
Answer:
The two digits are 42 and 24
Step by step explaination :
Let the two digit be x and y
∴ Number (2−digit) =10×x+y
Sum of 2 - digit and reverse of it
⟹10x+y+10y+x=66 (given)
∴x+y=6 (equation 1)
Digits differ by 2
∴x−y=2 (equation 2)
On adding,
2x=8
⟹x=4
∴y=2
or, x+y=6 From 1 equation
and y−x=2 From 2 equation
On adding:
2y=8
y=4
x=2