Question

i am a number greater than 40,000 and less than 60000. my ones digit and tens digit are the same. my ten thousand digit is 1 less than 3 times the sum of my ones digit and tens digit. my thousand digit is half my hundreds digit and the sum of these two digits is 9. what number am i?

Answer 1

Let ones and digits be = d ==> 10,000 digit = 3x(d + d) - 1 = 6d - 1

As number lies between 40 thousand and 60 thousand, 6d - 1 = 4 or 5.

6d - 1 = 4 => d = 5/6,  
Now d = 5/6 cannot be a digit.

6d - 1 = 5 ==> d = 6/6 = 1
==> Ones, Tens digits are = 1      ------------------(1)
and 10,000 digit = 6xd - 1 = 6x1 - 1 = 5.----------(2)

Let hundreds digit be = 2k, ==> Thousands digit = k
Also 2k + k = 9 => k = 9/3 = 3.
Hence hundreds digit = 6 and thousands digit = 3 ----------------------------------------(3) 

From (1), (2), (3), the number = 53611

Answer 2

Answer:

Step-by-step explanation:

Let ones and digits be = d ==> 10,000 digit = 3x(d + d) - 1 = 6d - 1

As number lies between 40 thousand and 60 thousand, 6d - 1 = 4 or 5.

6d - 1 = 4 => d = 5/6,  

Now d = 5/6 cannot be a digit.

6d - 1 = 5 ==> d = 6/6 = 1

==> Ones, Tens digits are = 1      ------------------(1)

and 10,000 digit = 6xd - 1 = 6x1 - 1 = 5.----------(2)

Let hundreds digit be = 2k, ==> Thousands digit = k

Also 2k + k = 9 => k = 9/3 = 3.

Hence hundreds digit = 6 and thousands digit = 3 ----------------------------------------(3)

From (1), (2), (3), the number = 53611