Question

$\text{Find the value of the letters in the following question:}$

$AB\times AB\underset{–}{}6AB\underset{–}{}$
[3 marks]

Answer 1

$\text{Given,}AB\times AB\underset{–}{}6AB\underset{–}{}$

$\text{i.e.}AB\times AB=6AB\text{Here,}B\times B\text{is a number whose units digit is}B.\text{Therefore,}B=0,1,5\text{or}6$
[1 mark]
$\text{Again,}AB\times AB=6AB\cdots \left(i\right)\Rightarrow \text{Then square of a two-digit number is a three-digit number.}\text{So,}A\text{can take values 1, 2 and 3.}$
[1 mark]
$\text{For}A=1,2,3\text{and}B=0,1\text{or}6,\text{Eq. (i) is not satisfied.}\text{We find that}A=2,B=5,\text{satisfies the Eq. (i).}$
[1 mark]
$\text{Hence,}A=2,B=5.$