Question

When a 4 digit number is multiplied by 9 its digits get reversed. Find the 4 digit number. Also, when a 5 digit number is multiplied by 9,its digit get reversed. What is this 5 digit number?

Answer 1

Given :   a 4 digit number is multiplied by 9 its digits get reversed.

To Find : the 4 digit number.

Solution:

ABCD  * 9  =  DCBA

A must be  1    as greater than 1 multiplied by 9 will result in 5 digit number

1BCD  * 9  = DCB1

D must be 9  as only 9 * 9  = 81  

=> 1 BC9  * 9  = 9CB1

C * 9  + 8  = 10X + B     X is carry over

B * 9 +  X  = C      and no carry over   as    1* 9 = 9 in last

so B must be 0

=> X = C

C * 9  + 8  = 10C + 0

=> C= 8

1089 * 9 = 9,801

1089 is 4 digit number

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