Question

A one digit number which is the ten's digit of a two digit number x, is substracted from x to give y which is the quetient of the division of 999 by the cube of a number. find the sum of the digits of x

Answer 1

Given : A one digit number which is the ten's digit of a two digit number x,  is substracted from x to give y which is the quotient of the division of 999 by the cube of a number.

To  find :   the sum of the digits of x

Solution:

two digit number x,  = AB

Tens digit = A

10A + B  -  A =  9A  + B

y = 9A + B

y    =  999 / z³

  999 = 3 * 3 * 3 * 37  = 3³ x 37

or  1 * 1 * 1 * 999  =  1³ x 999

y can not be  999

Hence  z = 3

=> y    =  999 / 3³  = 37

y = 9A + B  =  37

A = 4  and  B =  1

x  = 10A + B = 41

sum of digits of x = 4 + 1 = 5

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