The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.
The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.
Let digit at unit's place be u
digit at ten's place be t
Original number: 10t + 1u
When digits are reversed, the new number will have the values of the digits (represented by the variables) in reverse order:
new number: 10u + 1t
And this new number is twenty-seven more than the original number:
(new number) is (old number) increased by (twenty-seven)
10u + 1t = 10t + 1u + 27
10u + t = 10t + u + 27
9u – 9t = 27
u – t = 3 …..(1)
Sum of digits of a two digit number is 7
t + u = 7 … (2)
Solving Equations (1) and (2) by elimination method,
Add (1) and (2) equations ,
2u = 10
u = 5
Substitute u = 5 in equation (1)
5 - t = 3
t = 2
Hence , the number is 25.
Let digit at unit's place be u
digit at ten's place be t
Original number: 10t + 1u
When digits are reversed, the new number will have the values of the digits (represented by the variables) in reverse order:
new number: 10u + 1t
And this new number is twenty-seven more than the original number:
(new number) is (old number) increased by (twenty-seven)
10u + 1t = 10t + 1u + 27
10u + t = 10t + u + 27
9u – 9t = 27
u – t = 3 …..(1)
Sum of digits of a two digit number is 7
t + u = 7 … (2)
Solving Equations (1) and (2) by elimination method,
Add (1) and (2) equations ,
2u = 10
u = 5
Substitute u = 5 in equation (1)
5 - t = 3
t = 2
Hence , the number is 25.
