The units digit of a two digit number is 1 more than twice the tens digit. If the digits are reversed, the new number is 36 more than the original number. Find the number.

Question

asked Jan 24, 2021 94.5k views

1 Answer

Rajesh Narwal · Answer 1 · 2021-01-29T20:14:38+0000

Answer:

37

Explanation:

Let the initial number be
xy=10x+y .

Initial number:

Units digit = y

Tens digit = x

The units digit of a 2-digit number is 1 more than twice the tens digit, then

y=2x+1

Reversed number is
yx=10y+x.

If the new number is 36 more than the original number, then

(10y+x)-(10x+y)=36

Simplify this equation:

$10y+x-10x-y=36\\ \\9y-9x=36\\ \\y-x=4$

Substitute
y=2x+1 into the equation
y-x=4:

$(2x+1)-x=4\\ \\2x+1-x=4\\ \\x+1=4\\ \\x=3\\ \\y=2\cdot 3+1=7$

Initial number: 37