Question

Sum of the digits of a two digit number is 9. When we interchange the digits, it is found that the resulting number is greater than the original number by 27. What is the two digit number?​

Answer 1

Answer:

The two digit number is 36.

Solution :

Let,

• Units digit = x
• Tens digit = 9 - x

★ Original no. =

• 10 (9 - x) + x
• 90 - 9x

★ When we interchange the digits :

• 10x + (9 - x)
• 9x + 9

It is found that the resulting new number is greater than the original number by 27

⇒ 90 - 9x + 27 = 9x + 9

⇒ 90 + 27 - 9x = 9x + 9

⇒ 117 - 9x = 9x + 9

⇒ 117 - 9 = 9x + 9x

⇒ 108 = 18x

⇒ x = 108 / 18

⇒ x = 6

Units digit = 6

• Tens digit = 9 - x

⇒ 9 - 6

⇒ 3

Tens digit = 3

∴ The two digit number is 36.

Answer 2

Hello, Buddy!!

➸ ɢɪᴠᴇɴ:-

• Sum of the digits of a two digit number is 9.
• When the digits are interchanged, it is found that the resulting number is greater than the original number by 27.

➸ ᴛᴏ ꜰɪɴᴅ:-

• The two digit number.

➸ ʀᴇQᴜɪʀᴇᴅ ꜱᴏʟᴜᴛɪᴏɴ:-

Let,

The two digits of the given number be x and y

• Once Place digit be x
• Tens Place digit be y

Then, the original number is 10y+x

Now, the number obtained by interchanging the digits is

• y in once place & x in ten's place.

→ 10x+y

Given,

Sum of the digits of the number is 9

☞ x+y = 9 ➝ ①

The number obtained by interchanging the digits is 27 greater than the previous number

→ New Number = 27+Actual Number

→ 10x+y = 27+(10y+x)

→ 10x+y = 27+10y+x

→ 10x+y-(x+10y) = 27

→ 10x-x+y-10y = 27

→ 9x-9y = 27

→ 9(x-y) = 27

→ x-y = 27/9

→ x-y = 3 ➝ ②

By Adding equation ① & ②

→ (x-y)+(x+y) = 3+9

→ 2x = 12

→ x = 12/2

→ x = 6

• Value of x ☞ 6

By Substituting x = 6 in equation ①

→ x+y = 9

→ 6+y = 9

→ y = 9-6

→ y = 3

• Value of y ☞ 3

Actual Number ☞ 10y+x

→ 10(3)+6

→ 30+6

→ 36

• Unit's Digit ☞ 6
• Ten's Digit ☞ 3

The Required Two Digit Number

• $\longmapsto\;\Large{\red{\bold{36}}}$

$\boxed{\tt{@MrSovereign♡}}$

Hope This Helps!!