The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 165. What can be the original number?
Answers
Step-by-step explanation:
Let the two digit no. be 10X+Y
According to the statement
X - Y = 3. (statement 1)
after interchanging the digits the new number will be 10Y + X
According to the statement
10X + Y + 10Y + X = 165(statement 2)
=) 11X + 11Y = 165
=) X + Y = 15 (statement 2)
By adding statement 1 and statement 2 we get
2X = 18
=) X = 9
When substituting the value of X in statement 1 we get the value of Y as 6
Answer:
X=9
Y=6
and the original number is 96.(when X>Y)
and it is 69 when Y>X.
Answer:
let the digits of the number be x and y such that the number is (10x+y)
according to the question
case1 case2
x-y=3 ....1 y-x=3....1
10x+y+10y+x=165 10x+y+10y+x=165
11x+11y=165 11x+11y=165
11(x+y)=165 11(x+y)=165
x+y=165/11 x+y=165/11
x+y=15....2 x+y=15....2
from equation1 and 2
x+y=15-(x-y=3) x+y=15-(y-x=3)
x+y-x+y=15-3 x+y-y+x=15-3
2y=12 2x=12
y=6 x=6
x-y=3 y-x=3
x-6=3 y-6=3
x=3+6=9 y=3+6=9
therefore, the original number can be 96 or 69