Question

the sum of two digit number is 12 the digits are reversed the new number becomes 4/7 times the original number find the original number
for class 8th
ch=linear equations in one variable
so please use only one variable​

Answer 1

Solution :-

Let :-

Digit in ten's place = x

Digit in one's place = y

Two digit number = 10x + y

According to the first condition :-

$:\implies \sf x+y  = 12$

$:\implies \sf x = 12-y  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  ...................(1)$

According to the second condition :-

$:\implies \sf \dfrac{4}{7} \times 10x+y = 10y+x$

$:\implies \sf \dfrac{40x+4y}{7}= 10y+x$

$:\implies \sf 40x+4y = 70y+7x$

$:\implies \sf40x-7x+4y-70y = 0$

$:\implies \sf 33x-66y = 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  ..................(2)$

Substitute the value of x in eq(2) :-

$:\implies \sf 33(12-y)-66y = 0$

$:\implies \sf396-33y-66y = 0$

$:\implies \sf -99y = -396$

$:\implies \sf \bf y = 4$

Substitute y = 4 in eq(1) :-

$:\implies \sf x = 12-4$

$:\implies \bf x = 8$

Two digit number = 84

Answer 2

Step-by-step explanation:

Let

One's place digit=x

Ten's place digit =y

${:}\longrightarrow\sf the number =10y+x$

Condition-1:-

${:}\longrightarrow\sf x+y=12$

${:}\longrightarrow\sf y=12-x\dots\dots (1)$

Condition-2:-

if the digits reversed then the new number=10x+y

${:}\longrightarrow\sf \dfrac {4}{7}(10y+x)=10x+y$

${:}\longrightarrow\sf \dfrac {4 (10y+x)}{7}=10x+y$

${:}\longrightarrow\sf \dfrac {40y+4x}{7}=10x+y$

• use cross multiplication

${:}\longrightarrow\sf 40y+4x=7 (10x+y)$

${:}\longrightarrow\sf 40y+4x=70x+7y$

${:}\longrightarrow\sf 40y-7y+4x-70x=0$

${:}\longrightarrow\sf 33y-66x=0\dots (2)$

• Substitute the value of y from eq (1)

${:}\longrightarrow\sf 33(12-x)-66x=0$

${:}\longrightarrow\sf 396-33x-66x=0$

${:}\longrightarrow\sf 396-99x=0$

${:}\longrightarrow\sf -99x=-396$

${:}\longrightarrow\sf x=\dfrac {-396}{-99 }$

${:}\longrightarrow\sf x=4$

• Substitute the value in eq (1)

${:}\longrightarrow\sf y=12-4$

${:}\longrightarrow\sf y=8$

Hence the two digit number

${:}\longrightarrow\sf 10(8)+4$

${:}\longrightarrow\sf 80+4$

${:}\longrightarrow\sf 84$

$\therefore\underline{\sf The\:two\:digit\:number\:is\;84.}$