The sum of the digits of a 2 digit number is 10. If the digits are reversed, the number formed will be 54 more than the original number. Find the number? Explain with full procedure.
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let the two digit number be = 10x+y where y is at unit's place and x is at ten's place.
According to the question = x+y = 10 ------1st equation
and 10y+x =10x+y+54
= 10y-y+x-10x = 54
9y-9x = 54
y-x = 6 -----2nd equation
solving 1st and 2nd equation we get x=2
putting value of x on eq. 1 we get the value of y
x+y = 10
2+y =10
= y = 10-2
y=8
required number is 28.
According to the question = x+y = 10 ------1st equation
and 10y+x =10x+y+54
= 10y-y+x-10x = 54
9y-9x = 54
y-x = 6 -----2nd equation
solving 1st and 2nd equation we get x=2
putting value of x on eq. 1 we get the value of y
x+y = 10
2+y =10
= y = 10-2
y=8
required number is 28.
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