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

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

Step-by-step explanation:

Let the Digit in the units place of the Two Digit number be : A

Given : The Sum of the Digits of Two Digit number is 14

It means : The Digit in the Ten's place will be : 14 - A

★  The Two Digit Number can be written as : 10(14 - A) + A

Given : If 36 is added to the number, the Digits get interchanged

$\mathsf{\implies 10(14 - A) + A + 36 = 10(A) + (14 - A)}$

$\mathsf{\implies 140 - 10A + A + 36 = 10A + 14 - A}$

$\mathsf{\implies 176 - 9A = 9A + 14}$

$\mathsf{\implies 9A + 9A = 176 - 14}$

$\mathsf{\implies 18A = 162}$

$\mathsf{\implies A = 9}$

$\mathsf{\implies Ten's\;Place\;Digit = (14 - 9) = 5}$

Answer : The Two Digit Number is 59