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 54 find the original number check your solution
Answers
Answer:
The number if 39.
Step-by-step explanation:
Let the original number be, 10x + y.
Given:
x + y = 12...(i)
10y + x = 10x + y +54
9x - 9y = -54
x - y = -6...(ii)
Solve (i) and (ii) simultaneously as follows:
x + y = 12
x - y = -6
_______
2x = 6
x = 3
Substitute x = 3 in equation (i) and solve for y as follows:
x + y = 12
3 + y = 12
y = 12 - 3
y = 9
Thus, the number if 39.
Check:
x + y = 12
3 + 9 = 12
Hence proved.
Answer:
39
Step-by-step explanation:
Let the number at ten's place be = x
and at one's place = (12 - x)
Number formed = 10x + 12 - x
= 9x + 12.....................(1)
On reversing the digits we get the number = 10(12 - x) + x
= 120 - 9x...................(2)
It is given that 9x +12 + 54 = 120 - 9x
⇒ 9x + 9x = 120 - 12 - 54
⇒ 18x = 54
⇒ x = 3
Hence the number is 9 x 3 + 12 = 39.
On reversing the digits we get 93 and the difference of 93 and 39 is 54.
Hope it helps you...