Question

Question 56

Find the value of the letters in the following question:

$AB\times AB\_\_\_\_\_\_\_\_6AB$

Answer 1

Given, $AB\times AB\_\_\_\_\_\_\_\_6AB$
i.e. $AB\times AB=6AB$
Here, $B\times B$ is a number whose unit's digit is B. Therefore, B = 1 or 5 [$\because$ B $\ne$ 0, else AB $\times$ A + $\ne$ 6A]
Again, $AB\times AB=6AB$
$\Rightarrow$ Then square of a two-digit number is a three-digit number.
So, A can take values 1, 2 and 3.
For A = 1, 2, 3 and B = 1, Eq. (i) is not satisfied.
We find that A = 2, B = 5, satisfies the Eq. (i).
Hence, A = 2, B = 5