Question

In a two - digit number, unit's digit is twice the ten's digit. If sum of the digits is
added to the whole number, the result is equal to 30. Find the number.​

Answer 1

In a two - digit number, unit's digit is twice the ten's digit. If sum of the digits is

added to the whole number,

Answer 2

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Let's solve the problem now!!!

$\green{\large\underline{\sf{Solution-}}}$

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{digit \: at \: tens \: place = x} \\ &\sf{digits \: at \: ones \: place \: = 2x } \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: So - \begin{cases} &\sf{number \: formed = 10 \times x + 2x = 12x}\end{cases}\end{gathered}\end{gathered}$

According to statement,

Sum of the digits is added to the whole number, the result is equal to 30.

$\rm :\longmapsto\:x + 2x + 12x = 30$

$\rm :\longmapsto\:15x = 30$

$\rm :\longmapsto\:x = 2$

$\blue{\begin{gathered}\begin{gathered}\bf\: Hence-\begin{cases} &\sf{digit \: at \: tens \: place = 2} \\ &\sf{digits \: at \: ones \: place \: = 2 \times 2 = 4 } \end{cases}\end{gathered}\end{gathered}}$

$\red{\begin{gathered}\begin{gathered}\bf \: So - \begin{cases} &\sf{number \: formed = 12x = 12 \times 2 = 24}\end{cases}\end{gathered}\end{gathered}}$