Question

If a two-digit number is $\frac{3}{2}$ times the product of its digits and is four times the sum of its digits, then the two-digit number can be

• A. 36
• B. 45
• C. 48
• D. 56

Answer 1

The correct option is C 48

Let the two-digit number be of the form 10x + y, where, x is tens digit and y is unit digit According to the question,
$(10x+y)=\frac{3}{2}\left(xy\right)......\left(i\right)$
And, (10x + y) = 4(x + y) .......(ii)
From (ii),
10x + y = 4x + 4y
$\Rightarrow (10-4)x=(4-1)y$
$\Rightarrow 6x=3y$
$\Rightarrow y=2y.....\left(iii\right)$
Substituting the value of y in (i), we get
$(10x+2x)=\frac{3}{2}(x\times 2x)$
$\Rightarrow 12x=3x^2$
$\Rightarrow 3x^2-12x=0$
$\Rightarrow 3x(x-4)=0$
$\Rightarrow x=0orx=4$
When x = 4, then y = 8. [From (iii)] When x = 0, their will be no two-digit number.
Thus, the two-digit number can be (10 × 4) + 8 = 40 + 8 = 48.
Hence, the correct answer is option (3).