Question

In a two digit number, the ten's digit is 2 more than unit's digit. Sum of the digits is 1/7 of the whole number. Find the digits and number.​

Answer 1

Step-by-step explanation:

let tens digit is X

then unit digit = X-2

the no = 10X+X-2

according to question X+X-2=(11X-2)/7

SOLVING

14X-14=11X-2

3X= 12

X=4

unit digit 4-2=2

no = 42

hope it helps

SO NO IS

Answer 2

Basic Concept Used :-

Writing Systems of Linear Equations 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.

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

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

$\begin{gathered}\begin{gathered}\bf \: Hence-\begin{cases} &\sf{number \: formed=10y+x}\end{cases}\end{gathered}\end{gathered}$

According to statement,

The tens digit is 2 more than units digit

$\bf\implies \:y = x + 2 - - - (1)$

According to statement again,

Sum of the digits is 1/7 of the whole number.

$\rm :\implies\:x + y = \dfrac{1}{7} (10y + x)$

$\rm :\longmapsto\:7x + 7y = 10y + x$

$\rm :\longmapsto\:7x - x = 10y - 7y$

$\rm :\longmapsto\:6x = 3y$

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

$\rm :\longmapsto\:2x = x + 2 \: \: \: \: \: \: \bf\{using \: (1) \}$

$\bf\implies \:x = 2$

On substituting the value of x = 2, in equation (1), we get

$\bf\implies \:y = 4$

$\begin{gathered}\begin{gathered}\bf\: It \: means-\begin{cases} &\sf{digit \: at \: unit \: place = 2} \\ &\sf{digit \: at \: tens \: place = 4} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: Hence-\begin{cases} &\sf{number \: formed=10y+x = 40 + 2 = 42}\end{cases}\end{gathered}\end{gathered}$