Question

The sum of the digits of a
two-digit number 12 ,if the
digits are reversed, the new number is 4/7 the times the original number Determine the original number​

Answer 1

Answer:

${\underline{\boxed{\sf\green{Original \: \: Number \: \: = \: \: 84}}}}$

Step-by-step explanation:

Given:-

• Sum of digits of two-digit number = 12
• Digits reversed,new number = 4/7 times original number.

To find:-

• The original number = ?

Let the one's digit be a and ten's digit be b.

$\therefore\bold\blue{Original \: number = a + 10b}$

A/Q,

1st case:-

$\longrightarrow\tt\ a + b = 12 \\\\\longrightarrow\large\tt\green{a = 12 - b..........(i)}$

$\rule{100}{1}$

2nd case:-

$\longrightarrow\tt 10a + b = \dfrac{4}{7}(a + 10b) \\\\\longrightarrow\tt 10a + b = \dfrac{4a + 40b}{7} \\\\\longrightarrow\tt 7(10a + b) = 4a + 40b \\\\\longrightarrow\tt 70a + 7b = 4a + 40b \\\\\longrightarrow\tt 70a - 4a = 40b - 7b \\\\\longrightarrow\tt 66a = 33b \\\\\tt\pink{\: \: \: \: From\:(i): a = 12 - b }\\\\\longrightarrow\tt 66(12 - b) = 33b \\\\\longrightarrow\tt 792 - 66b = 33b \\\\\longrightarrow\tt 66b + 33b = 792 \\\\\longrightarrow\tt 99b = 792 \\\\\longrightarrow\tt b =\cancel{\dfrac{792}{99}}\\\\\longrightarrow\large{\boxed{\bold\red{b = 8 }}}$

$\rule{200}{1}$

$\star\textsc{Putting \: value \: of \: b \: in \: (i) }$

$\longrightarrow\tt a = 12 - 8 \\\\\star\large{\boxed{\bold\blue{a = 4 }}}$

$\rule{100}{2}$

* Number :-

$\longrightarrow\tt Original \: number = a + 10b \\\\\longrightarrow\tt Original \: number = 4 + 10(8)$

$\star\large\tt\gray{Original \: number}$ = $\large{\boxed{\sf\pink{ 84 }}}$

${\underline{\boxed{\therefore{\sf\blue{Original \: number = 84 }}}}}$

Answer 2

Step-by-step explanation:

Here you go ☆☆

▪let digit at ones place = x

and at tens place= y

▪so, no. is 10y + x

▪given, y+x= 12------《1》

▪if no. is reversed , then

▪10x+ y = 4/7(10y +x)

▪10x-4/7x + y -40/7y

66/7x-33/7y = 0

▪multiply term with 7 , we get ,

▪66x -33y = 0

taking 33 as common,

▪2x -y =0------《2》

▪by elimination method,

multiply 1 by 2 and subtract 2 from 1 ,we get,

▪2x +2y =24

▪2x - y = 0

- + -

▪3y = 24

▪y = 8

▪so x= 4

▪so original no.= 84

hope it helps you....