In a 3 - digit number unit's digit, ten's digit and hundred's digit are in the ratio 1:2:3. If the difference of an original number and the number obtained by reversing the digits is 594. Find the number.

A three digit number can be expressed as 100x + 10y + z where x = hundred's digit, y = 10 digit and z = unit digit.

Eg - : 356 = 100(3) + 10(5) + 6

Ratio of digits = 1:2:3

Let ratio be a

Unit digit = a

Ten's digit = 2a

Hundred's digit = 3a

It means that ten’s digit is double of unit digit and hundred’s digit is triple of unit digit.

Difference of original number and the number obtained by reversing the digit is 594.

If number 100x + 10y + z is reversed

New number will be 100z + 10y + x

Eg - : like when a number is in its original form it is 356 and now when it is reversed then it will be 653 which is equal to 100(6) + 5(10) + 3

∴ Original number – New number = 594

100x + 10y + z – (100z + 10y + x) = 594

100x + 10y + z – 100z – 10y – x = 594

99x – 99z = 594

x – z = 6

x = hundred's digit

z = unit digit

From above, we know that hundred’s digit is triple of the unit digit that is hundred's digit = 3z

So, 3z – z = 6

2z = 6

z = 3

Therefore, unit digit = 3

Ten's digit = 6 (as it is double of unit digit)

Hundred's digit = 9 (as it is triple of unit digit)

Therefore, the number is 963.