NIMCET 2018 Question Paper with solutions

Since, a number in base if can only have digits from 0 to (K -1), we can conclude that
x ≥ 5 and y ≤ 7
Now, the original equation, when converted to decimal base gives:
$4{\mathit{x}}^1$ + 3x° = $\mathit{y}\left(8^1\right)$ + 3 (8°)
⇒ 4x + 3 = 8y + 3
⇒ x = 2y
So, we have the following constraints
x ≥ 5
y ≤ 7
x = 2y, x and y are integers.
The set of values of (x, y) that satisfy these constraints are:
(6, 3), (8, 4), (10, 5), (12, 6), (14, 7)
So, the number of possible solution is 5,