While multiplying B and 5 we are getting a number whose ones digit is B again.

This is only possible when B = 5 or B = 0

In that case,

The product will be, B × 5 = 5 × 5 = 25

2 will be a carry for the next step

Now,

We have, 5 × A + 2 = CA, which is possible for A = 2 or 7

The multiplication is as follows:

If B = 0,

B × 5 = B

⇒ 0 × 5

= 0

There will not be any carry in this step.

In the next step, 5 × A = CA

It can only happen when A = 5 or A = 0

But, A cannot be 0 as AB is a two-digit number

Hence, A can be 5 only.

The multiplication is as follows:

Hence, there are 3 possible values of A, B, and C:

(i) 5, 0, and 2 respectively

(ii) 2, 5, and 1 respectively

(iii) 7, 5, and 3 respectively

6