If you multiply the four-digit number abcd by 4, the order of digits will be reversed. that is, abcd x 4=dcba. the digits a, b, c and d are all different. find abcd. that means what numbers are abcd equal to?

The number is 2178, multiplied by 4 gives 8712.

Step-by-step explanation:

Let us say the number is written as abcd   .....(1)

When you multiply it by 4, it gives dcba

Now,

We get;

=>

=>     ......(2)

Now, we can relate few properties:

The first digit is a quarter of the last one as d=4a .

or

or

The second digit is one less than the first.  

Now, from equation 2, we get

Replacing b and d, we get

=>

=>

or,

There is only one single digit integer solution.

c = 7; a = 2

Now,  

=1 and  d =4(2) =8

Hence, 2178 is the number.

And we can see that

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step-by-step explanation: