Find the value of $A$ in the following
$A 36 - 1 A 4 = 742$

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Solution

We know that we can write a number by multiplying its digits with the place value.
So,
$A 36$ can be written as $= A \times 100 + 3 \times 10 + 6 = 100 A + 36$
and $1 A 4$ can be written as $1 \times 100 + A \times 10 + 4 = 10 A + 104$
So,
$\Rightarrow 100 A + 36 - (10 A + 104) = 742$
$\Rightarrow 100 A + 36 - 10 A - 104 = 742$
$\Rightarrow 90 A = 742 + 104 - 36$
$\Rightarrow 90 A = 846 - 36$
$\Rightarrow 90 A = 810$
$\Rightarrow A = 9$

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