Question

Sum of the digits of a two-digit number
is 5. When we interchange the digits, it is
found that the resulting new number is
less than the original number by 27.
What is the two-digit number?​

Answer 1

Answer:41

Step-by-step explanation:

let the no. be 10x + y

acco. to question x+y= 5

i.e., x=5-y.....(1).......also acco. to question 10y+x=10x+y-27............(2)

On substituting (1) in (2), we get:

10y+5-y=10(5-y)+y-27

9y+5=50-10y+y-27

9y+9y=50-27-5

18y=18

y=1..............and

x=5-y=4

no. is 10(4)+1

=40+1=41

Answer 2

ANSWER:-

Two digit number is 41

$\rule{200}2$

EXPLANATION:-

Given:-

• Sum of the digits of a two-digit number is 5.
• When we interchange the digits, it is found that the resulting new number is less than the original number by 27.

To Find:-

Two digit number.

Solution:-

Let tens digit number be x and one's digit number be y.

Number = 10x + y

$\underline{\underline{\red{ \sf{According\:to\:question\::}}}}$

Sum of digits is 5.

$\implies\:\sf{x\:+\:y\:=\:5}$

$\implies\:\sf{x\:=\:5-\:y}$......(1)

$\underline{\underline{\red{ \sf{According\:to\:question\::}}}}$

When we interchange the digits, it is found that the resulting new number is less than the original number by 27.

Two digit number after interchanging = 10y + x

$\implies\:\sf{10y+x\:=\:10x+y-27}$

$\implies\:\sf{10y-y+x-10x\:=\:-27}$

$\implies\:\sf{9y-9x\:=\:-27}$

$\implies\:\sf{9(y-x)\:=\:-27}$

$\implies\:\sf{y-x\:=\:-3}$.......(2)

Substitute x = 5-y in (eq 2)

$\implies\:\sf{y-(5-y)\:=\:-3}$

$\implies\:\sf{y-5+y\:=\:-3}$

$\implies\:\sf{2y\:=\:2}$

$\implies\:\sf{y\:=\:1}$

Substitute y = 1 in (eq 1)

$\implies\:\sf{x\:=\:5-1}$

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

So,

Ten's digit = x = 4

One's digit = y = 1

•°• $\underline{\sf{Two\:digit\:number\:=\:41}}$