Question

number of natural number such that it is 11 times the sum of its digits​

Answer 1

Given : natural number such that it is 11 times the sum of its digits

To Find : How many such numbers

Solution:

1 digit numbers not possible

2 digits numbers

Let say number is xy

sum of digits = x + y

number = 10x + y

10x + y = 11(x + y)

10x + y = 11 x + 11y

x = -10y

hence not possible

three digit numbers

11x + 11y + 11z = 100x + 10y + z

89x = y+ 10z

x = 1 , y = 9 , z = 8

198 is such a tumber

four digit Number

1000x + 100y + 10z + w = 11(x + y + z + w)

not possible

Hence 198 is the only number

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