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fredd [130]
3 years ago
14

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?
Mathematics
2 answers:
kogti [31]3 years ago
6 0

Answer:

The number is 2178, multiplied by 4 gives 8712.

Step-by-step explanation:

Let us say the number is written as abcd (1000a+100b+10c+d)   .....(1)

When you multiply it by 4, it gives dcba (1000d+100c+10b+a)

Now, 4\times(abcd)=dcba

We get;

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

=> 3999a+390b=996d+60c

=> 1333a+130b= 20c+332d     ......(2)

Now, we can relate few properties:

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

or a=d/4

or a=0.25d

The second digit is one less than the first.  

b=(a-1)

Now, from equation 2, we get

1333a+130b= 20c+332d

Replacing b and d, we get

1333a+130a-130=20c+1328a

=> 135a=20c+130

=> 27a=4c+26

or, a =(4/27)c+(26/27)

There is only one single digit integer solution.

c = 7; a = 2

Now,  

b =2-1=1 and  d =4(2) =8

Hence, 2178 is the number.

And we can see that 4\times2178= 8712

Arisa [49]3 years ago
5 0
The given is that A B C D <span>x 4 = D C B A
</span><span>
Possible values of A are 1 or 2. It can't be 1 since the </span><span> </span><span>final result A is in unit place and 1 is not possible when we multiply any number by 4
</span><span>
2 B C D x </span><span>4 = </span><span>D C B 2</span>
It is clear above, that D = 8
2 B C 8 x <span>4 = </span><span>8 C B 2</span>
Possible values of B should be 1 or 2
We try B=1

2 1 C 8 x <span>4 = </span><span>8 C 1 2

</span>To find for C, you can use the equation:

(2000+100+10C+8) x 4 = 8000+100C+10+240C = 432-12 = 420
Therefore,

C = 7
So, the number is 2178.
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