Given: The number is multiplied by 561 and the result obtained is 32,582. But it was found that both 2 in the number are wrong.

Let's assume the number to be "abcdefg". We know that the product of this number and 561 is 32,582. So we can write it as:

abcdefg × 561 = 32,582

We can simplify this equation by dividing both sides by 561:

abcdefg = 32,582 / 561

abcdefg = 58.117

Now we know that both 2 in the number are wrong. Let's assume that the correct digits are x and y. So the correct number will be:

abcde(x)y × 561 = 32,582

We can simplify this equation by dividing both sides by 561:

abcde(x)y = 32,582 / 561

abcde(x)y = 58.117

Now we need to find the values of x and y that satisfy this equation. We can do this by trial and error, or we can use some algebraic manipulation.

Let's first consider the units digit. We know that the units digit of the correct number multiplied by 561 should be equal to the units digit of 32,582. The units digit of 32,582 is 2, so the units digit of the correct number should be:

(x × 1 + y × 6) mod 10 = 2

We can simplify this equation by using modular arithmetic:

x + 6y ≡ 2 (mod 10)

Now let's consider the tens digit. We know that the tens digit of the correct number multiplied by 561 should be equal to the tens digit of 32,582, which is 8. The tens digit of 561 is 6, so we can write:

(x × 6 + y × 5 + carry) mod 10 = 8

Here, carry is the carry-over digit from the units place. Since we know that the units digit of the correct number is x + 6y - 10 (from the previous equation), we can substitute this value:

((x × 6 + y × 5 + x + 6y - 10) div 10) + ((x × 6 + y × 5 + x + 6y - 10) mod 10) = 8

We can simplify this equation by using modular arithmetic:

7x + 12y ≡ 58 (mod 100)

Now we have two equations with two variables:

x + 6y ≡ 2 (mod 10)

7x + 12y ≡ 58 (mod 100)

We can solve these equations using the Chinese remainder theorem or by trial and error. The solution is x = 7 and y = 9, which gives us the correct number:

abcde79 × 561 = 37,586,119

Therefore, the correct answer is option (b) 37,587.