Question

one of the two digit of a two digit number is three times the other digit if you interchange the digits of this two digit number and add the resulting number to the original number you get 88 what is the original number ​

Answer 1

GIVEN:

• One of the two digit of a two digit number is three times the other digit
• If the digits are interchanged and resulting number is added to original number we get 88

TO FIND:

• What is the original number ?

SOLUTION:

Let the digit at unit's place be 'y' and the digit at ten's place be 'x'

❖ NUMBER = 10x + y

CASE:- 1)

❒ One of the two digit of a two digit number is three times the other digit

According to question:-

➸ x = 3y....❶

CASE:- 2)

❒ If the digits are interchanged and resulting number is added to original number we get 88

☆ Reversed Number = 10y + x

☆ Resulting Number + Original Number = 88

According to question:-

➸ 10y + x + 10x + y = 88

➸ 11x + 11y = 88

Take 11 common from both sides

➸ x + y = 8....❷

Put the value of 'x' from equation 1) in equation 2)

➸ 3y + y = 8

➸ 4y = 8

➸ y = $\sf{\cancel\dfrac{8}{4}}$

❮ y = 2 ❯

On putting the value of 'y' in equation 1), we get

➸ x = 3 $\times$ 2

❮ x = 6 ❯

☆ NUMBER = 10x + y

☆ NUMBER = 10(6) + 2

☆ NUMBER = 60 + 2

☆ NUMBER = 62

❝ Hence, the number formed is 62 ❞

______________________

Answer 2

Solution :

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

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

A/q

$\longrightarrow\sf{r=3m................(1)}$

&

$\longrightarrow\sf{10r+m + 10m+r = 88}\\\\\longrightarrow\sf{10r + r + m + 10m = 88}\\\\\longrightarrow\sf{11r + 11m=88}\\\\\longrightarrow\sf{11(r+m)=88}\\\\\longrightarrow\sf{r+m=\cancel{88/11}}\\\\\longrightarrow\sf{r+m=8}\\\\\longrightarrow\sf{3m+m=8\:\:[from(1)]}\\\\\longrightarrow\sf{4m=8}\\\\\longrightarrow\sf{m=\cancel{8/4}}\\\\\longrightarrow\bf{m=2}$

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

$\longrightarrow\sf{r=3(2)}\\\\\longrightarrow\bf{r=6}$

Thus;

$\boxed{\sf{The\:original\:number=10r+m=[10(6) + 2]=[60+2]= \boxed{\bf{62}}}}$