a sum of two digit number is 20.When 9 is added to the number,thenumbers interchange their places.Find the number
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Let the digit in tens place be x and digit in the ones place be y.
Number= 10x+y
x+y=20 (equation I)
(10x+y)+9=10y+x(equation ii)
=10x-x+9=10y-y
=9x+9=9y
y=(9x+9)/9(equation iii)
Putting the value of y in equation I, we get
x+(9x+9)/9=20
9x+9x+9/9=20
18x+9=180
18x=171
x=9.5
Substituting the value of x in equation iii, wer get
y=9*9.5+9/9
y=855+9/9
y=864/9
y=96
Number=191
Number= 10x+y
x+y=20 (equation I)
(10x+y)+9=10y+x(equation ii)
=10x-x+9=10y-y
=9x+9=9y
y=(9x+9)/9(equation iii)
Putting the value of y in equation I, we get
x+(9x+9)/9=20
9x+9x+9/9=20
18x+9=180
18x=171
x=9.5
Substituting the value of x in equation iii, wer get
y=9*9.5+9/9
y=855+9/9
y=864/9
y=96
Number=191
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