Q5 of 23 Page 1

Attempt any two subquestions from the following:

A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number, the digits are interchange. The addition of first and third digit is 1 less than middle digit. find the number.

Given: three digit number

Let the number is xyz. i.e. the numerical value is 100x + 10y + z.


Acc to given conditions:


100x + 10y + z + 198 = 100z + 10y + x


⇒ 100(x-z) + z-x = -198


⇒ 99(z-x) = 198


⇒ z-x = 2 …(1)


Also,


x + z = y – 1 …(2)


add (1) and (2)


2z = y + 1 …(3)



Now put these values in equ. 2 to find value of x



Reject the negative values of x hence (1,5,3), (2,7,4), (3,9,5) will be possible.


So candidates are (153, 274, 395)


Only 153 is divisible by 17.


Hence the ans is 153.


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