This question is based on the five, three-digit numbers given below.
(Left) 324 523 643 136 441 (Right)
(Example- 697 – First digit = 6, second digit = 9 and third digit = 7)
(NOTE: All operations to be done from left to right.)

If 3 is added to the first digit of every number, in how many numbers will the first digit be exactly divisible by the second digit?

The correct answer is 2.

Let's analyze the given set of five three-digit numbers step-by-step from left to right:

Given numbers: 324, 523, 643, 136, 441

We are asked to add 3 to the first digit of every number and then check in how many of the resulting numbers the new first digit is exactly divisible by its second digit.

1. First number: 324
- First digit = 3, Second digit = 2
- Add 3 to the first digit: 3 + 3 = 6
- Check divisibility: Is 6 divisible by 2? Yes ($\frac{6}{2}=3$ with a remainder of 0).
- Result: Valid

2. Second number: 523
- First digit = 5, Second digit = 2
- Add 3 to the first digit: 5 + 3 = 8
- Check divisibility: Is 8 divisible by 2? Yes ($\frac{8}{2}=4$ with a remainder of 0).
- Result: Valid

3. Third number: 643
- First digit = 6, Second digit = 4
- Add 3 to the first digit: 6 + 3 = 9
- Check divisibility: Is 9 divisible by 4? No (9 divided by 4 leaves a remainder of 1).
- Result: Invalid

4. Fourth number: 136
- First digit = 1, Second digit = 3
- Add 3 to the first digit: 1 + 3 = 4
- Check divisibility: Is 4 divisible by 3? No (4 divided by 3 leaves a remainder of 1).
- Result: Invalid

5. Fifth number: 441
- First digit = 4, Second digit = 4
- Add 3 to the first digit: 4 + 3 = 7
- Check divisibility: Is 7 divisible by 4? No (7 divided by 4 leaves a remainder of 3).
- Result: Invalid

Comparing all numbers, there are exactly 2 numbers (324 and 523) where the modified first digit is divisible by the second digit.