A four-digit number gets reversed when it is multiplied by 4. find the sum of the digits of the number.

Let the number be 'abcd'. We can write as 1000a+100b+10c+d. According to the question: (1000a+100b+10c+d)x4=1000d+100c+10b+a We get as 3999a+390b-60c-996d=0 Use hit and trial : Take a=2,b=1,c=7,d=8.The above condition gets satisfied. Now add the values of a,b,c,d.That will be your answer. Answer:18

for hit and trial it will take time is there another method