Question

the sum of the digits of a two-digit number is 14. if 36 is added to the number its digits are interchanged.find the number

Answer 1

Answer:

59

Step-by-step explanation:

 Let the required number be ab which can be written as 10a + b.

Given,

        sum of digits = 14

         ⇒ a + b = 14

         ⇒ a = 14 - b

According to question : 36 is added to the number its digits are interchanged. So the new number will be ba or 10b + a.

 ⇒ Orig. no. + 36 = new no.

 ⇒ 10a + b + 36 = 10b + a

 ⇒ 36 = 10b + a - 10a - b

 ⇒ 36 = 9b - 9a

 ⇒ 36 = 9( b - a )

 ⇒ 4 = b - a

             a = 14 - b

⇒ 4 = b - ( 14 - b )  ⇒ 4 = b - 14 + b

  ⇒ 4 + 14 = 2b  ⇒ 18 = 2b

  ⇒ 9 = b

Hence,   a = 14 - 9 = 5

  Required number is ab = 59

Answer 2

AnswEr:

Required number is 59.

ExplanaTion:

Let the two digit number be xy.

Number = 10x + y

According to the question,

x + y = 14

→ x = 14 - y..........(1)

Also, it is given that, if 36 is added to number, it's digits will interchange.

→ 36 + 10x + y = 10y + x

→ 36 + 10x - x = 10y - y

→ 36 + 9x = 9y

→ 9y - 9x = 36

Taking 9 as common,

→ y - x = 4...........(2)

Put the value of (1) in (2).

→ y - (14 - y) = 4

→ y - 14 + y = 4

→ 2y - 14 = 4

→ 2y = 4 + 14

→ 2y = 18

→ y = $\dfrac{18}{2}$

→ y = 9

Now, put the value of y in (1).

→ x = 14 - 9

→ x = 5

Hence, required number is 59.