Question

3. Given that 45 is the difference between a number and that
digits of the number is 13. then find the number.
and the answer is 49​

Answer 1

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

Correct question :-

Given that 45 is the difference between a number and that formed by reversing it's digit. if the sum of digit of the number is 13 then find the number

Given :-

• 45 is the difference between a number and that formed by reversing it's digit.
• The sum of digit of the number is 13

To find :-

• The number.

Solution :-

Let the digit in the units place be x

Let the digit in the tens place be y

As per the first condition,

Original two digit number = 10y + x

Reversed two digit number = 10x + y

Difference = 45

Let's represent this condition mathematically,

Place the reversed two digit number at the forefront of the whole equation,

(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 ----->1

As per the second condition,

• The sum of digit of the number is 13

So, here we can form our 2nd equation,

x + y = 13 ---->2

Add equation 1 to 2, and solve them simultaneously,

x - y = 5

x + y = 13

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

2x = 18

x = $\bf\large\frac{18}{2}$

x = 9

•°•Number in the units place = x = 9

Substitute, x = 9 in equation 1

x - y = 5

9 - y = 5

- y = 5 - 9

- y = - 4

y = 4

•°•Number in the tens place = y = 4

Number formed = 49

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

For first case :-

• 45 is the difference between a number and that formed by reversing it's digit

Number = 94

Reverse = 49

Difference = 45

$\bf\implies$ 94 - 49 = 45

$\bf\implies$ 45 = 45

LHS = RHS.

For second case :-

• The sum of digit of the number is 13,

Number = 49

Sum = 13

$\bf\implies$ 4 + 9 = 13

$\bf\implies$ 13 = 13

LHS = RHS.

Hence answer is verified.