The digit of a two-digit number in the tens place is 5 more than the digit in the ones place. If the digits are reversed, and the number so formed is added to fifteen times the digit in the unit’s place of the original number, then it is found to be equal to the original number. Find the number.
Answers
Answer: 83
Step-by-step explanation:
For example : 67 can be written as 6*10+7. Similarly,
Let original number have x as the ten's digit and y as the unit's digit. (xy)
the number's value is 10x+y.
When number is reversed, y is the ten's digit and x is the unit's digit. (yx)
so the number's new value is 10y+x.
It's given that (10y+x)+15*y=(10x+y). Upon simplifying
8y=3x or y=3/8x
We know that x and y are whole numbers varying from 0 to 9. If x is not a multiple of 8, then the RHS of above equation becomes a fraction which is not possible since y is a whole number. Thus 8 divides x. We also know that x is a single digit number, so ultimately x has to be 8 (x can't be 0 as it is given that the original number is a 2-digit number). Therefore y=3/8*8=3
Therefore, original number is xy i.e. 83.
You can verify this answer by doing the operations mentioned in the qn.
In this way, we don't even need the first line of information. You can verify that the tens digit is 5 more than the unit's digit.