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 \(4\times2178= 8712\)
