Question

A two-digit number is 3 more than 4 times the sum of its digit. If 18 is added to the number, the digits are reversed. Find the number.

Answer 1

Gɪᴠᴇɴ :-

A two-digit number is 3 more than 4 times the sum of its digit. If 18 is added to the number, the digits are reversed.

ᴛᴏ ғɪɴᴅ :-

• Original number
• Reversed number

sᴏʟᴜᴛɪᴏɴ :-

Let the tens place digit be x and ones place be y

then,

➥ Original number = (10x + y)

✞ According to 1st condition :-

• Original no = 3 + 4(Sum of digits)

➱ 10x + y = 3 + 4(x + y)

➱ 10x + y = 3 + 4x + 4y

➱ 10x - 4x + y - 4y = 3

➱ 6x - 3y = 3

➱ 3(2x - y) = 3

➱ 2x - y = 3/3

➱ 2x - y = 1

➱ y = 2x - 1. ---(1)

➥ Reversed Number = (10y + x)

✞ According to 2nd condition :-

• Original no + 18 = Reversed no

➱ 10x + y + 18 = 10y + x

➱ 10x - x + y - 10y = -18

➱ 9x - 9y = -18

➱ 9(x - y) = -18

➱ x - y = -18/9

➱ x - y = -2

➱ y = x + 2. ---(2)

From (1) and (2) , we get,

➱ 2x - 1 = x + 2

➱ 2x - x = 2 + 1

➱ x = 3

Put x = 3 in (1) , we get,

➱ y = 2x - 1

➱ y = 2×3 - 1

➱ y = 6 - 1

➱ y = 5

Hence,

• Tense place digit = x = 3
• Ones place digit = y = 5

Therefore,

• Original number = 10x + y = 35
• Reversed number = 10y + x = 53

Answer 2

Answer:

Given:

• A two-digit number is 3 more than 4 times the sum of its digit. If 18 is added to the number, the digits are reversed.

Find:

• Find the number.

According to the question:

• Let us assume m and n as tens and units digit and (10m + n) be the number.

Calculations:

⇒ $\sf{10m + n = 4 (m + n) + 3}$

⇒ $\sf{10m + n = 4m + 4n + 3}$

⇒ $\sf{6m - 3n = 3}$  

⇒ $\sf{2m - n = 1 \: --- \:Equation \: (1)}$

We know that:

⇒ $\sf{(10m + n + 18) = (10y + m)}$

⇒ $\sf{9m - 9n = -18}$

⇒ $\sf{m - n = -2}$ --- Equation (2)

Subtracting Equation (ii) with (i), we get:

⇒ ${\sf{\underline{\boxed{\green{\sf{ m = 3}}}}}}$

Adding values form the above equation, we get:

⇒ $\sf {2m - n = 1}$

⇒ $\sf{ 2 \times 3 - n = 1}$

⇒ $\sf{n = 6 - 1}$

⇒ ${\sf{\underline{\boxed{\green{\sf{ n = 5}}}}}}$

Therefore, the required numbers values are m = 3 and n = 5

⇒ $\sf{(10n + n) = (10(3) + 5)}$

⇒ $\sf{30 + 5}$

⇒ ${\sf{\underline{\boxed{\green{\sf{ 35 }}}}}}$

Therefore, 35 is the number.

According to the question, reversing 35 we get 53, and 53 is the required answer.