Question

8. The sum of the digits of a two-digit number is 14. The number obtained by inter-changing the digits is 36 more than the given number. Find the number.​

Answer 1

Answer:

59

Step-by-step explanation:

Let the number be 10x + y

Given that sum of the digits of a 2 digit number is 14.

Therefore, x + y = 14.............(1)

Given that the number obtained by interchanging the digits is 36 more than the given number.

The reverse of 10x + y number is 10y + x

Therefore, 10y + x = 10x + y + 36

=> 9y – 9x = 36

=> y – x = 4..........(2)

Adding (1) and (2) we get

2y = 18 => y = 9

=> x = 14 – 9 = 5

Therefore, the number is 10(5) + 9 = 59

I hope this will be help you.

Answer 2

GivEn:

• The sum of the digits of a two-digit number is 14.
• The number obtained by inter-changing the digits is 36 more than the given number.

To find:

• The original number?

Solution:

☯ Let the digit at ten's place and one's place be x and y respectively.

Therefore,

• Original number = 10x + y
• Reversed number = 10y + x

Given that,

• The sum of the digits of a two-digit number is 14.

x + y = 14

x = 14 - y⠀⠀⠀⠀⠀⠀⠀ ❲eq (1)❳

★ According to the Question:

• The number obtained by inter-changing the digits is 36 more than the given number.

➯ 10y + x = 10x + y + 36

➯ 10y + x - 10x - y = 36

➯ 9y - 9x = 36

➯ 9(y - x) = 36

➯ y - x = 36/9

➯ y - x = 4⠀⠀⠀⠀⠀⠀⠀ ❲eq (2)❳

⠀━━━━━━━━━━━━━━━━━

Substituting eq (1) in eq (2),

➯ y - (14 - y) = 4

➯ y - 14 + y = 4

➯ 2y - 14 = 4

➯ 2y = 18

➯ y = 18/2

➯ y = 9

Now, Substitute value of y in eq (1),

➯ x = 14 - 9

➯ x = 5

Therefore,

• Original number, (10x + y) = 10 × 5 + 9 = 59
• Reversed number, (10y + x) = 10 × 9 + 5 = 95