Name: Problem Based on Formation of Quadratic Equation
Uploaded: 2019-07-19
Duration: 5 min 41 s
Description: In this video, we will learn to solve a problem from the chapter Quadratic Equations, where we need to form an equation whose roots are given. Let's watch an...

Question

A two-digit number is

4

times the sum of its digits and twice the product of its digits. Find the number.

Accepted Answer

Let the digits in ones and tens place be $y$ and $x$ .

The required two-digit number is $(10 x + y)$

By the given data, the two-digit number is $4$ times the sum of its digits. We can write,

$(10 x + y) = 4 (x + y)$

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

$\Rightarrow 10 x + y - 4 x - 4 y = 0$

$\Rightarrow 6 x - 3 y = 0$

$\Rightarrow 2 x - y = 0$

$\Rightarrow 2 x = y \dots . . (1)$

By the given data two-digit number is twice the product of its digits.

$(10 x + y) = 2 x y \dots . . (2)$

By substituting the value of $y$ in equation $(2)$ , we get,

$(10 x + 2 x) = 2 x \times 2 x$

$\Rightarrow 12 x = 4 x^{2}$

$\Rightarrow 4 x^{2} - 12 x = 0$

$\Rightarrow 4 x (x - 3) = 0$

$\Rightarrow x (x - 3) = 0$

$\Rightarrow x = 0 or x - 3 = 0$

$\Rightarrow x = 3$ or $x = 0$

As $x = 0$ is not possible, as it won’t fit our assumption.

When $x = 3$ , $y = 2 x = 2 \times 3 = 6$ .

Thus, the required number is $(10 x + y) = (10 \times 3 + 6) = 36$ .

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

Important Questions on Quadratic Equations

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