Question

ABCD×4=DCBA, What is that number of ABCD?

Answer 1

Here we go. 

Your number 'abcd'  can be written as
1000a+100b+10c+d ....... (1)

Similarly, number 'dcba' can be written as 1000d+100c+10b+a .......(2)

Given: abcd*4 = dcba

Now, abcd must be less than 2500, because 2500*4 = 10000; which is a 5-digit number. 

So,  'a' can be either 1 or 2. But a multiple of 4 has to be even, therefore 'a' = 2.

Now, the value of 'd' has to be 8; because 'a' i.e. 2 times 4 is 8.

Now, putting values of 'a' and 'd' in (1) and (2):

4000a+400b+40c+4d = 1000d+100c+10b+a

you'll get, 13b=2c-1

The only possible value of 'b' and 'c' to satisfy this equation by being single integers is

'b' = 1 and 'c' = 7.

So, 
The number 'abcd' becomes 2178.
The number 'dcba' becomes 8712

2178*4 = 8712.