sum it the digits of a 2 digit number is10. when we interchange the digits. it is found times that resulting new number is smaller than original number by 18. find the two digit number.
Answers
Answer:
Let the digits at units and tens place in the given number be x and y respectively. Then,
Number =10y+x (i)
Number formed by interchanging the digits =10x+y
According to the given conditions, we have
(10y+x)+(10x+y)=110
and, (10y+x)−10=5(x+y)+4
⇒11x+11y=110
and, 4x−5y+14=0
⇒x+y−10=0
and, 4x−5y+14=0
By using cross-multiplication, we have
14−50
x
=
−40−14
y
=
−5−4
1
⇒
−36
x
=
−54
y
=
−9
1
⇒x=
−9
−36
and y=
−9
−54
⇒x=4 and y=6.
Putting the values of x and y in equation (i), we get
Number =10×6+4=64.
Step-by-step explanation:
Pleasemark as Brainlist answer
Answer:
Step-by-step explanation:
let x = tens digit
and 10 - x = ones digit
original no . = 10 x + 10 - x
on interchanging digits , no formed =
10 [ 10 - x ] + x = 100 - 10 x + x
ATQ ,
100 - 10 x + x + 18= 10 x + 10 - x
118 - 9 x = 9x + 10
118 - 10 = 9 x + 9x [ by interchanging sides ]
108 = 18 x
108 /8 = x
6 = x
hence the original no . = 10 x + 10 - x
10 [ 6 ] + 10 - 6
= 60 + 4
= 64