The sum of the digits of a two-digit number is 7. if the digits are reversed, the difference between the new number and the original number is 9. Find the original number?
Answers
Answer:
→ The original number is 34 .
Step-by-step explanation:
Let the unit's digit of the original number be x .
And, the ten's digit of the original number be y .
Now, A/Q,
→ Sum of the two digits number is 7 .
∵ x + y = 7 ............(1) .
Original number = 10x + y .
Number obtained on reversing the digits = 10y + x .
A/Q,
→ If the digits are reversed, the difference between the new number and the original number is 9.
∵ ( 10y + x ) - ( 10x + y ) = 9 .
⇒ 10y + x - 10x - y = 9 .
⇒ - 9x + 9y = 9 .
⇒ 9( - x + y ) = 9 .
⇒ - x + y = 9/9 .
∵ - x + y = 1 ...........(2) .
On substracting equation (1) and (2), we get
x + y = 7 .
- x + y = 1 .
+ - -
________
⇒ 2x = 6 .
⇒ x = 6/2 .
∴ x = 3.
On putting the value of 'y' in equation (1), we get
∵ x + y = 7 .
⇒ 3 + y = 7 .
⇒ y = 7 - 3 .
∴ y = 4 .
Therefore , the original number = 10x + y .
= 10 × 3 + 4 .
= 30 + 4 .
= 34 .
Hence, the original number is 34 .
THANKS .
Let the first digit = x ---(1)
Then the second digit is = y
According to the question ,
x+y = 7
And
Original Number = 10x+y
Then the number is reversed ,
10y+x
Given that ,
(10y+x)-(10x+y) = 9
10y+x-10x-y = 9
9y-9x = 9
9(y-x) = 9
(y-x) = 1 => -x+y = 1 => -(x-y) = 1 => x-y = -1 ---(2)
Adding Equation 1 and 2 ,
x+y = 7
x-y = -1
_________
2x = 6
_________
x = 6/2 = 3
Putting x = 3 in eq. 1 , we get
x+y = 7
3+y = 7
y = 7-3 = 4
The required number =
10x+y = 3×10+4 = 34