The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 18, find the original number.
Answers
Answer:
Original number = 57
Step-by-step explanation:
Given:
- Sum of the digits of the number is 12
- New number formed is greater than the origial number by 18
To Find:
- The original number
Solution:
Let us assume the unit's digit of the number as x.
Let us assume the ten's digit of the number as y
Hence the original number will be,
Original number = 10y + x
But by given,
x + y = 12
x = 12 - y------(1)
Now the reversed number is given by,
Reversed number = 10x + y
By given,
Reversed number = Original number + 18
Substitute the data,
10x + y = 10y + x + 18
Substitute the value of x from equation 1
10(12 - y) + y = 10y + 12 - y + 18
120 - 10y + y = 9y + 30
120 -9y = 9y + 30
9y + 9y = 120 - 30
18y = 90
y = 90/18
y = 5
Hence the ten's digit of the number is 5.
Now substitute the value of y in equation 1
x = 12 - 5
x = 7
Therefore the digit in the unit's number is 7.
Hence,
Original number = 10y + x
Original number = 10 × 5 + 7
Original number = 57
Therefore the original number is 57.
Verification:
Sum of the digits = 12
5 + 7 = 12
12 = 12
Reversed number = Original number + 18
10x + y = 10y + x + 18
10 × 7 + 5 = 10 × 5 + 7 + 18
75 = 57 + 18
75 = 75
Hence verified.