Question

The digit at the tens place of a two digit number is 4 times the digit at ones place if the sum of this number and the number formed by reversing the digit is 55 find the number​.

What's the correct answer is

Only explained answer ......​

Answer 1

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: AnSwer :- \: \star}}}}}$

Given :

The digit at the tens place of a two digit number is 4 times the digit at ones place.

The sum of this number and the number formed by reversing the digit is 55.

To Find :

The original two digit number.

Solution :

Let the digit at the tens place be x.

Let the digit at the units place be y.

Original Number = (10x + y)

Case 1 :

The digit at the tens place is 4 times the digit at the ones place.

Equation :

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

$\sf{x=4y}$

Case 2 :

The sum of original number and the number formed by reversing the digit is 55.

Reversed Number = (10y + x)

Equation :

$\sf{\longrightarrow{10x+y+10y+x=55}}$

$\sf{\longrightarrow{10x+x+10y+y=55}}$

$\sf{\longrightarrow{11x+11y=55}}$

$\sf{\longrightarrow{11(x+y)=55}}$

$\sf{\longrightarrow{x+y=\dfrac{55}{11}}}$

$\sf{\longrightarrow{x+y=5}}$

$\sf{\longrightarrow{4y+y=5}}$

$\bold{\big[From\:equation\:(1)\:x\:=\:4y\:\big]}$

$\sf{\longrightarrow{5y=5}}$

$\sf{\longrightarrow{y=\dfrac{5}{5}}}$

$\sf{\longrightarrow{y=1}}$

Substitute, y = 1 in equation (1),

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

$\sf{\longrightarrow{x=4(1)}}$

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

$\large{\boxed{\tt{Tens\:digit\:=\:x\:=\:4}}}$

$\large{\boxed{\tt{Units\:digit\:=\:y\:=\:1}}}$

$\large{\boxed{\tt{Original\:Number=\:10(x)+y=10(4)+1=40+1=41}}}$

Hope it helps you..

Answer 2

$\huge\underline\mathbb{\red S\pink {0} \purple {L} \blue {UT} \orange {1}\green {ON :}}$

Let the digit at one's place be x.

The digit at ten's place=4x

Therefore, the two digit number=10(4x) +x=40x+x=41x

On reversing the number,the digit at one's place =x

And the digit at ten's place=4x

So, the two digit no.=10(x)+4x

=10x+4x=14x

=According to the question,

=41x+14x=55

=55x=55

=x=55/55

=>x=1

The two digit number=>41x

=>41*1=41

hence,

the two digit number is 41..