A two digit number is four times the sum and three times the product of its digits. Find the number.

Open in App

Solution

Let the digits at tenth and units place of the number be $x$ and $y$ respectively. Then, Number $= 10 x + y$

It is given that
Number $= 4 \times$ sum of digits. also, Number $= 3 \times$ product of digits

$\Rightarrow 10 x + y = 4 (x + y); 10 x + y = 3 x y$

$\Rightarrow 6 x - 3 y = 0; 10 x + y = 3 x y$

$\Rightarrow y = 2 x; 10 x + y = 3 x y$

$\Rightarrow 10 x + 2 x = 3 x \times 2 x \Rightarrow 6 x^{2} - 12 x = 0 \Rightarrow 6 x (x - 2) = 0 \Rightarrow x = 0 o r x = 2$

Since the given number is a two digit number, its tenth digit cannot be zero
$∴$ $x = 2 \Rightarrow= 2 \times 2 = 4$

Hence, the required number $= 10 x + y = 10 \times 2 + 4 = 24$

Suggest Corrections

Similar questions

If two digit number is four times the sum of its digits and twice the product of digits .find the number

A two-digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

Join BYJU'S Learning Program