Q13/033) Find a 3 digit number which equals sum 17 times the hundredth digit, 34 times tens digits and 51 times the units digit.

Let the digits be xyz

So the number = 100x + 10y + z = 17 x + 34 y + 51 z

Or 83 x = 24 y + 50 z  (1)

Working in mode 24 we have 11 x = 2z

So x is even

  X =2 => z = 11 not possible

X= 4 => z = 10 not possible

X = 6 => Z = 9 ( and from (1) 24 y = 83 x- 50 z = 498 – 540 = 48 or y = 2)

X = 8=> z = 8 ( and from(1) 24 y = 33 * 8 or y > 10)

So the number is 629