Question

sum of digits of two -digit number is 9. the number obtained by interchanging the digit exceeds the given number by 27 . find the given number



answer please​

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

The sum of digits of two - digit number is 9, the number obtained by interchanging the digit exceeds the given number by 27.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The number.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the ones place digit be r

Let the tens place digit be m

$\underline{\sf{The\:original\:number=\pink{10m+r}}}\\\underline{\sf{The\:reversed\:number=\pink{10r+m}}}$

A/q

$\leadsto\sf{r+m=9}\\\\\leadsto\sf{m=9-r..........................(1)}$

&

$\longrightarrow\sf{10m+r=10r+m+27}\\\\\\\longrightarrow\sf{10m-m+r-10r=27}\\\\\\\longrightarrow\sf{9m-9r=27}\\\\\\\longrightarrow\sf{9(m-r)=27}\\\\\\\longrightarrow\sf{m-r=\cancel{\dfrac{27}{9} }}\\\\\\\longrightarrow\sf{m-r=3}\\\\\\\longrightarrow\sf{9-r-r=3\:\:\:\:[from(1)]}\\\\\\\longrightarrow\sf{9-2r=3}\\\\\\\longrightarrow\sf{-2r=3-9}\\\\\\\longrightarrow\sf{-2r=-6}\\\\\\\longrightarrow\sf{r=\cancel{\dfrac{-6}{-2} }}\\\\\\\longrightarrow\sf{\pink{r=3}}$

Putting the value of r in equation (1),we get;

$\longrightarrow\sf{m=9-3}\\\\\longrightarrow\sf{\pink{m=6}}$

Thus;

$\underbrace{\bf{The\;original\:number\:10m+r=10(6)+3=60+3=\boxed{63}}}}}$

Answer 2

Answer:

Step-by-step explanation:

Smaller number = 17

larger number = 26

Given numbers are (Let) a, b., let “a” be the smaller number and “b” be the larger..

given “a + b = 43” this is eq 1

Given “The smaller number is 9 less than the larger number”

=> b - a = 9

so, “b = 9 + a” this is eq 2

Substitute eq 2 in 1

This gives a + 9 + a = 43

=> 2a + 9 = 43

=> 2a = 43 – 9

=> 2a = 34

so, “a = 17” and “b=26”:

2