Sum of digits of a two-digit number is 9. when we interchange the digits, it is found that the resulting new number is greater than the original number by 27. what is the two-digit number?
Answers
Let one digit be x and the other be y
Number is 10x+y
Also x+y=9
or y=9-x.... (i)
According to question,
10y+x=10x+y+27..... (ii)
Putting (i) on (ii)
10(9-x)+x=10x+9-x+27
90-10x+x=9x+36
90-9x=9x+36
54=18x
x=3
Therefore the number is 10(3)+9-3=36
Answer is 36
Answer:
The Original Number is 36.
Given :
Sum of the Digits = 9
The number with interchanged digits is greater than the original number by 27.
To Find :
The Number
Solution :
Orignal Number,
- Units place as x
- Tens place as 10(9 - x)
⇒x + 10(9 - x)
⇒ x + 90 - 10x
⇒ -9x + 90 ......... [ Original Number ]
Number with reversed digits,
- Units Place = (9 - x)
- Tens Place = 10(x)
⇒ 9 - x + 10x
⇒ 9 + 9x .......... [ Number with Reversed Digits ]
The number with interchanged digits is greater than the original number by 27.
⇒ 9x + 9 = ( –9x + 90) + 27
⇒ 9x + 9 = - 9x + 117
⇒ 9x + 9x = 117 - 9
⇒ 18x = 108
⇒ x = 108/18
⇒ x = 6
Units Place = 6
★ Value of 10(9 - x)
⇒ 10(9 - 6)
⇒ 10(3)
⇒ 30
The Original Number -
⇒ 30 + 6
⇒ 36
The Original Number is 36