The sum of the digits of a two-digit number is 15. If the digits are reversed the new number is nine less than

Question

The sum of the digits of a two-digit number is 15. If the digits are reversed the new number is nine less than the original number. Find the original number.

Answer 1

ab

a + b = 15 ===> a = 15 - b ----------(1)

10b + a = (10a + b) - 9 -------------(2)

subst (1) into (2),

10b + 15 - b = 150 - 10b + b - 9

9b + 15 = 141 - 9b

18b = 126

b = 7 (ans)


subst into (1),

a = 15 - 7 = 8 (ans)

therefore, ab = 87

Answer 2

let the digits of the ten"s and unit's place be respetively x and y
hence,the number is 10x+y
According to the conditions.
x+y=15.....(1)
10y+x=10x+y-9....(2)
From 2,we get,
10y+x-10x-y=-9
=>. -9x+9y= -9
=>x-y=1
adding with this eqn no 1
2x=16
=>x=8
putting the value of x in eqn 1,we get
y=7
Therefore,the original no. is 87

Answer 3

87

8 + 7 = 15

87-78=9

Answer 4

x + y = 15
10y + x = (10x + y) + 9
==>
10y + 15 - y = 150 - 10y + y + 9
9y + 15 = 159 - 9y
18y = 144
y = 8
x = 7

Answer 5

87 &78