Question

A natural number is made up of four digits in ap having the sum 20. The number obtained by reversing the digits is 6174 more than the given number. Find the given number.

Answer 1

Answer:

let the original number be 4a+6d=20-----eq(1)

2a+3d=10-----eq(2)

let the original number be 1111a+123d

given that the number obtained by reversing the digit is 6174 more than original number

therefore

1111a+123d +6174 =1111a+3210d

this implies 123d+6174=3210d

6174=3210d -123d

6174 =3087d

6174/3087=d

therefore d=2

put d=2 in eq(2)

this give 2a+3(2) =10

2a=10-6=4

a =2

thus the original number is 2468