SOLUTION: The ones digit of a two-digit number is 4 times the tens digit. If the digits are reversed, the new number is 54 more than the original number. Find the number.

Question 131994: The ones digit of a two-digit number is 4 times the tens digit. If the digits are reversed, the new number is 54 more than the original number. Find the number.
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SOLUTION -
Let the digit at once place be x
and the digit at tens place be y
Number=10y+x
Reversing number=10x+y
According to the condition we have
x=4y .....(i)
According to the second condition we have
10x+y=10y+x+54
10x+y-10y-x=54
9x-9y=54
x-y=6 (dividing whole equation by 9)
substituting the value of x from equation (i) we have
4y-y=6
3y=6
=
y=2
substituting the value of y in equation (i) we have
x=4y
x=4*2
x=8
therefore
number is 10y+x=10*2+8=28

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