2. Sum of the digits of a two digit number is 7.When we interchangethe

1.	2. Sum of the digits of a two digit number is 7.When we interchangethe digits, it is found that the resulting new number is greaterthan the original number by 45. What is the two-digit number?
Answer» Answer : The required TWO DIGIT number is 16 Given : Sum of the digits of a two digit number is 7 When the digits are interchanged , it is found that resulting new number is greater than the original number by 45. To Find : The two digit number Solution : Let US consider the digits be x and y respectively Therefore , the two digit number is $\sf \dashrightarrow 10x + y$ According to question $\sf \implies x + y = 7......(1)$ Again by question $\sf \implies 10y + x = 10x + y + 45 \\\\ \sf \implies 10y - y + x - 10x = 45 \\\\ \sf\implies 9y - 9x = 45\\\\ \sf \implies 9(y-x)=45\\\\ \sf\implies y - x = 5 ........(2)$ Adding (1) and (2) we have , $\sf \implies x + y + y - x = 7+5\\\\ \sf\implies 2y = 12 \\\\ \sf\implies y = 6$ Putting the value of y in (1) $\sf\implies x + 6 = 7 \\\\ \sf \implies x = 7-6\\\\ \sf\implies x = 1$ Thus , the required number is $\sf\dashrightarrow 10\times1+6\\\\ \sf\dashrightarrow 16$ Read more about similar type of question , the link is provided below : brainly.in/question/18000883

2. Sum of the digits of a two digit number is 7.When we interchangethe digits, it is found that the resulting new number is greaterthan the original number by 45. What is the two-digit number?

Answer»

Answer :

The required TWO DIGIT number is 16

Given :

Sum of the digits of a two digit number is 7
When the digits are interchanged , it is found that resulting new number is greater than the original number by 45.

To Find :

The two digit number

Solution :

Let US consider the digits be x and y respectively

Therefore , the two digit number is

$\sf \dashrightarrow 10x + y$

According to question

$\sf \implies x + y = 7......(1)$

Again by question

$\sf \implies 10y + x = 10x + y + 45 \\\\ \sf \implies 10y - y + x - 10x = 45 \\\\ \sf\implies 9y - 9x = 45\\\\ \sf \implies 9(y-x)=45\\\\ \sf\implies y - x = 5 ........(2)$

Adding (1) and (2) we have ,

$\sf \implies x + y + y - x = 7+5\\\\ \sf\implies 2y = 12 \\\\ \sf\implies y = 6$

Putting the value of y in (1)

$\sf\implies x + 6 = 7 \\\\ \sf \implies x = 7-6\\\\ \sf\implies x = 1$

Thus , the required number is

$\sf\dashrightarrow 10\times1+6\\\\ \sf\dashrightarrow 16$

Read more about similar type of question , the link is provided below :

brainly.in/question/18000883