Question

the sum of digit of two digit is 15 the number obtained by inter changing the digit xceeds the given number by 9 find the number.​

Answer 1

Answer:

80 + 7 = 87. Sum of digits of a two-digit numbers is 15. The number obtained by interchanging its digits exceeds the given number by 9. Hence, the original number is 78.

Step-by-step explanation:

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Answer 2

SOLUTION :

Let the ten's digit number be r

Let the one's digit number be m

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

A/q

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

&

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

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

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

Thus;

The number = 10r + m = [10(7) + 8] = [70 + 8] = 78