Question

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

Answer 1

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 :

https://brainly.in/question/18000883

Answer 2

Consider the digits be x and y respectively.

Therefore, the two digit number is 10x+y.

According to the question :-

x+y=7 (1)

10y+x=10x+y+45

10y-y-x=10x=45

9y-9x=45

y-x=5 (2)

Add (1)&(2):-

x+y+y-x=7+5

2y=12

y=6

Putting the value of y in 1.

x+6=7

x=7-6

x=1

Thus, the required number is:-

10*1+6

=16