A number of two digits is increased by 36 when the digits are reversed. the sum of the digits is 10. Find the number.
37 is the number you seek. When this number is reversed, the number 73 is created; 37 + 36 = 73. Thus 37 is increased by 36 when the digits are reversed. And, the sum of 3 + 7= 10.
The number is 37.
37 + 36 = 73
7 + 3 =10
let X be the number in units place and Y be the number in the tens place
The sum of the digits in a two-digit is 7 and can be expressed as:
X+Y=10- eqn 1
When the digits are reversed, it can be expressed as this:
But, you also kow that when the digits are reversed, a number of two digits is increwased by 36 so:
10X+Y=10Y+X+36- eqn 2
Using the first equation, make X as the subject, so:
X=10-Y- eqn 3
Sub eqn 3 to eqn 2:
Sub. Y=3 ino eqn 1
As X= number in units place and Y= number in tens place, so
the two digit number would be 37
Double-check for mistakes:
the sum of digits of 37= 3+7=10 (correct)
When digit is reversed, 73
Compare the two numbers: 73 and 37
The difference between the two numbers
= 36 (correct)
In all, 37 is the two-digit number.