Question

A two digit number has tens digit greater than the unit digit if the sum of its digits is equal to twice the difference, then find the total number of such numbers possible.

Answer 1

Hint: To solve this question we will suppose 2-digit number as ‘ab’ where ‘a’ is the digit at tens place and ‘b’ is the digit at unit place. After that we will make an equation according to the condition given in the question. And then we will simplify the equation to get the value of a in terms of b, and then we will put the values in b such that values of a is less than 10 otherwise the number will become a 3-digit number. After finding the values of b we will find values of a for each b and count the number of cases formed to get the answer.

Complete step by step answer:
We are given a two digit number whose tens digit is greater than the unit digit if the sum of its digit is equal to twice the difference,
So we will suppose the number as ‘ab’,
Where ‘a’ is the digit at tens place and ‘b’ is the digit at ones place,
So now according to the question we are given that,
a > b,
and
( a+ b ) = 2 ( a – b )
a + b = 2a – 2b
a = 3b
Now we know that ‘a’ is the digit at tens place of a two digit number so it cannot be greater than 10, otherwise number will become a 3-digit number, so we have this condition now that,
a < 10
if a is less than 10 then b can only take values 1, 2, and 3 for all other positive values of a will be greater than 10,
so we have three values of b and that are 1, 2 and 3 and using the equation a = 3b three values of a will be 3, 6 and 9

so there are total three numbers that can be formed using the conditions given in the question and that are 31, 62 and 93.

Note: Whenever questions involving statements are given try to convert the given statements to the equations otherwise you may make mistakes while solving and end up with the wrong answer. For example this question cannot be solved using only guessing in mind in that case it is almost certain that you will miss some values so don’t try to use shortcuts here.