The digits of a two-digit number differ by 6. If the digits are interchanged and the resulting number is added to the original number, we get 110. What is the original number 2.
Answers
Answer:
85 and 58
Step-by-step explanation:
Let the digits of the number be a and b such that the number is (10a+b).
According to the question,
a−b=6 or b−a=6 ____ (1)
10a+b+10b+a=110
a+b=16 _____(2)
Solving both the equations, we have
a=8 and b=5 or a=5 and b=8
Therefore, the required number is 85 or 58.
Answer:
The original number is 82.
Step-by-step-explanation:
Let the greater digit at tens place be x.
And the smaller digit at units place be y.
∴ The two digit number = xy
⇒ Original number = 10x + y
From the first condition,
x - y = 6
⇒ x = 6 + y
⇒ x = y + 6 - - - ( 1 )
Now,
The number obtained by interchanging the digits = yx
⇒ New number = 10y + x
From the second condition,
Original number + New number = 110
⇒ 10x + y + 10y + x = 110
⇒ 11x + 11y = 110
⇒ x + y = 10 - - - [ Dividing by 11 ]
⇒ y + 6 + y = 10 - - - [ From ( 1 ) ]
⇒ 2y = 10 - 6
⇒ 2y = 4
⇒ y = 4 ÷ 2
⇒ y = 2
By substituting y = 2 in equation ( 1 ), we get,
x = y + 6 - - - ( 1 )
⇒ x = 2 + 6
⇒ x = 8
Now,
Original number = 10x + y
⇒ Original number = 10 * 8 + 2
⇒ Original number = 80 + 2
⇒ Original number = 82
∴ The original number is 82.