Question

In a two digit number the sum of the digit is 15 when the number reverse the number increased by 27 find the Number

Answer 1

S O L U T I O N :

Let the ten's digit number be r

Let the one's digit number be m

$\boxed{\bf{The\:original\:number=10r+m}}}}}\\\boxed{\bf{The\:reversed\:number=10m+r}}}}}$

A/q

$:\implies\sf{r+m=15}\\\\:\implies\sf{r=15-m.....................(1)}$

&

$:\implies\sf{10r+m+27=10m+r}\\\\:\implies\sf{10r-r+m-10m=-27}\\\\:\implies\sf{9r-9m=-27}\\\\:\implies\sf{9(r-m)=-27}\\\\:\implies\sf{r-m=\cancel{-27/9}}\\\\:\implies\sf{r-m=-3}\\\\:\implies\sf{15-m-m=-3\:\:\:[from(1)]}\\\\:\implies\sf{15-2m=-3}\\\\:\implies\sf{-2m=-3-15}\\\\:\implies\sf{-2m=-18}\\\\:\implies\sf{m=\cancel{-18/-2}}\\\\:\implies\bf{m=9}$

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

$:\implies\sf{r=15-9}\\\\:\implies\bf{r=6}$

Thus;

$\underbrace{\sf{The\:number\:(10r+m)=[10(6)+9]=[60+9]=\boxed{\bf{69}}}}}}$

Answer 2

Answer:

Step-by-step explanation:

Let us assume, x and y are the two digits of a number

Therefore, The two digit number is = 10x + y and the reverse number is 10y + x

Given:

x + y = 15 ---------1

y = 15 - x

Also given:

10x + y - 27 = 10y + x

9x - 9y = 27

x - y = 3  -----------2

Adding equation 1 and 2

2x = 18

x = 9

Therefore, y = 15 - x = 15 - 9 = 6

The two digit number is = 10x + y = (10 * 9) + 6 = 96

And the reverse number = 10y + x = (10 * 6) + 9 = 69

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