Question

A three digit number is such that twice the hundreds digits is thrice the hundred digit when they are reversed, it is increased by 594 find the number

Answer 1

Let's call the three-digit number ABC, where A represents the hundreds digit, B represents the tens digit, and C represents the units digit
According to the given information:

1. "Twice the hundreds digit is thrice the hundred digit when they are reversed" can be written as 2A = 3C.
2. "It is increased by 594" means ABC + 594.
   Now, let's solve this system of equations:
   From 1: 2A = 3C
   From 2: ABC + 594
   We can use the fact that ABC is a three-digit number, so A cannot be 0. We'll start by trying values of A from 1 to 9.
   For A = 1:
   2(1) = 3C
   2 = 3C
   C = ²/3 (not an integer, so A = 1 doesn't work)
   For A = 2:
   2(2) = 3C
   4 = 3C
   C = ⁴/₃ (not an integer)
   For A = 3:
   2(3) = 3C
   6 = 3C
   C = ⁶/₃ = 2
   Now that we have found C = 2, we can find B:
   From the equation ABC + 594:
   32B + 594
   Since we know B is a digit, B can be any integer from 0 to 9.
   For B = 0:
   32(0) + 594 = 594 (not a three-digit number)
   For B = 1:
   32(1) + 594 = 626 (not a three-digit number)
   For B = 2:
   32(2) + 594 = 658 (a three-digit number)
   So, the three-digit number ABC is 658.