Question

The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?

Answer 1

Answer:

The number can be 49 or, 94

Step-by-step explanation:

Let the ones digit be x and tens digit be y

Their sum is 13 (given)

So, x + y = 13........eq.(i)

The number can be formed is

(10*x) + (y*1)

= 10x + y

Interchanging the digits :

10y + x

According to the question :

$\sf : \implies \: (10x + y ) - (10y - x) = 45 \\ \sf : \implies \: 9x - 9y = 45 \\ \sf : \implies \: 9(x - y) = 45 \\ \sf : \implies \: x - y = \frac{45}{9} \\ \sf : \implies \: x - y = 5 ......eq.(ii)$

Now,

Substraction of both the equation :

$\sf \: x +y = 13 \\ { \sf{ \underline{ \: x - y = 5}}} \\ \sf : \implies \: 2x = 8 \\ \sf : \implies \: x = \frac{8}{2} \\ \sf : \implies \: x = 4 \: ans.$

Substituting the value of x in equation (i) :

$\sf : \implies \: x + y = 13 \\ \sf : \implies 4 + y = 13 \\ \sf : \implies \: y = 13 - 4 \\ \sf : \implies \: y = 9 \: ans.$

Hence,

The number is

10x + y = (10*4) + (9*1) = 40 + 9 = 49 or, 94

Answer 2

Given: The number obtained by interchanging its digits is 45 less than the original number and the sum of the digits is 13

To find: The original number

Solution: Let the digit in the tens place be x and the digit in the units place y.

Hence, the original  number = 10x + y

After interchanging the digits, new number = 10y + x

According to the question,

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

⇒ 9x -9y = 45

⇒ x - y = 5 [equation i]

Also given, x + y = 13 [equation ii]

Now adding the two equations,

2x = 18

⇒ x = 9

Putting the value of x in equation ii,

y = 13 - 9 = 4

Therefore, the original number = 10 × 9 + 4 = 94

Answer: 94