Question

17. The sum of the digits of a two digit number is 15. The number obtained by interchanging the
digits exceeds the given number by 9. The number is
a) 96
b) 69
c) 87
d) 78
pls tell me fast​

Answer 1

Solution :

Let the ten's place digit number be r & one's place digit be m;

$\boxed{\bf{Original\:number=10r+m}}}}\\\boxed{\bf{Reversed\:number=10m+r}}}}$

A/q

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

&

$\longrightarrow\sf{10m+r=10r+m+9}\\\\\longrightarrow\sf{10m-m+r-10r=9}\\\\\longrightarrow\sf{9m-9r=9}\\\\\longrightarrow\sf{9(m-r)=9}\\\\\longrightarrow\sf{m-r=\cancel{9/9}}\\\\\longrightarrow\sf{m-r=1}\\\\\longrightarrow\sf{m-(15-m) = 1\:\:[from(1)]}\\\\\longrightarrow\sf{m-15+m=1}\\\\\longrightarrow\sf{2m=1+15}\\\\\longrightarrow\sf{2m=16}\\\\\longrightarrow\sf{m=\cancel{16/2}}\\\\\longrightarrow\bf{m=8}$

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

$\longrightarrow\sf{r=15-8}\\\\\longrightarrow\bf{r=7}$

Thus;

$\boxed{\sf{The\:number=10r+m=[10(7) + 8 ] = [70 + 8]=\bf{78}}}}$

Option (d)

Answer 2

Step-by-step explanation:

Let the unit digit be x and tens place be y

x+y = 15 -------(i)

10 x + u - 10 y - x = 9

9x + 9y = 9

x - y = 1 ---------(ii)

By substraction

x+y-x+y = 15- 1

2y = 14

y = 7

From equation (i)

x+y = 15

x+7 = 15

x = 15-7

= 8

Number = 10y +x

10×7+8= 78