Question

a 2 digit number is 4 times the sum of its digit and twice the product of its digit.find the no
a 2 digit no is 5 times sum of its digit and is also equal to 5 more than twice the product of itsdigit.find the no

Answer 1

Dear student
Que1

Let the digit at units place = y

and digit at tens place = x

Therefore, the original number becomes = 10x+y

According to first condition

10x+y = 4(x + y)

⇒10x+y=4x+4y

⇒10x-4x= 4y-y

⇒6x = 3y

or

y = 2x.....(i)

According to second condition :

10x+y = 2xy

⇒10x+2x = 2x(2x) [From(i)]

$$\begin{gathered} \Rightarrow 4{\mathrm{x}}^2=12\mathrm{x} \\ \Rightarrow {\mathrm{x}}^2-3\mathrm{x}=0 \\ \Rightarrow \mathrm{x}\left(\mathrm{x}-3\right)=0 \\ \Rightarrow \mathrm{x}-3=0\mathrm{or}\mathrm{x}=0 \\ \Rightarrow \mathrm{x}=3\mathrm{or}\mathrm{x}=0\left(\mathbf{rejected}\right) \end{gathered}$$

Now, from (i), we get,

y = 2(3)

y = 6

Thus, the number = 10x+y = 10(3) +6=30+6=36

For remaining queries we request you to post them in separate threads to have rapid assistance from our experts.

Regards