Question

A natural number is made up of 4 digits of A.P, having sum 20. The number obtained by reversing the digits is 6174 more than given number. Find the number. ​

Answer 1

Answer:

2468

Step-by-step explanation:

Let the numbers in AP be a-3d, a-d, a+d, a+3d

Their Sum is 20

Therefore, 4a=20

a=5

Therefore the number is,

1000(a+3d)+100(a+d)+10(a-d)+a-3d

1000a+3000d+100a+100d+10a-10d+a-3d

1111a+3087d

The reverse of the number is

1000(a-3d)+100(a-d)+10(a+d)+a+3d

1111a-3087d

Therefore,

1111a+3087d=1111a-3087d-6174

6174d=-6174

d=-1

Therefore, the digits are 2,4,6,8

and the number is 2468