Question

if the sum of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45then the number is​

Answer 1

Answer:

72

Step-by-step explanation:

Let x and y be the digits

x+y = 9  ==========> Equation 1

(10x+y) - (10y+x) = 45

9x - 9y = 45

x - y = 5  =============> Equation 2

Solve both the equations

x + y = 9

x - y = 5

--------------

2x = 14 => x = 7, y = 2

Hence number is 72.

Answer 2

$\bf{\huge{\underline{\boxed{\rm{\red{Answer:}}}}}}$

Given :-

• The sum of a two digit number is 9
• The difference between the number and that formed by reversing the digits is 45

Solution :-

Let the digit in the tens place be x

Let the digit in the units place be y

Original two digit number = 10x + y

As per the first condition,

• The sum of a two digit number is 9

x + y = 9 ---->1

As per the second condition,

• The difference between the number and that formed by reversing the digits is 45

Reversed two digit number = 10y + x

Difference = 45

Let's represent this mathematically!

(10x + y) - ( 10y + x) = 45

10x + y - 10y - x = 45

10x - x - 9y = 45

9x - 9y = 45

9 (x - y) = 45

x - y = $\bf\large\frac{45}{9}$

x - y = 5 ---->2

Add equation 1 to 2,

x + y = 9

x - y = 5

--------------

2x = 14

x = $\bf\large\frac{14}{2}$

x = 7

•°• number in tens place of the two digit number = 7

Substitute, x = 7 in equation 2,

x - y = 5

7 - y = 5

- y = 5 - 7

- y = - 2

y = 2 [cancelling "-" from both sides]

•°• number in the units place of the two digit number is 2

•°•Number = 72

$\bf{\huge{\underline{\boxed{\rm{\blue{Verification:}}}}}}$

For first case :-

• the sum of a two digit number is 9

Two digit number = 72

Their sum = 9

7 + 2 = 9

9 = 9

LHS = RHS

For second case :-

• the difference between the number and that formed by reversing the digits is 45

Number = 72

Reversed number = 27

Difference= 45

$\bf\implies$72 - 27 = 45

$\bf\implies$ 45 = 45

LHS = RHS.

Hence answer is verified.