Question

The sum of the digits of a two digit number is 7
If the digits are reversed, the number is reduced
by 27. Find the number,​

Answer 1

Answer:

★ Number is 25 ★

Step-by-step explanation:

Given:

• Sum of digits of two digit number is 7
• After reversing digits the number is reduced by 27

To Find:

• What is the number?

Solution: Let the tens digit and unit digit of the number be x and y

→ x + y = 7.............(1)

A/q

→ The two digit number is 10x + y and after reversing it's digit the number becomes 10y + x

$\small\implies{\sf }$ 10y + x = 10x + y + 27

$\small\implies{\sf }$ 10y – y = 10x – x + 27

$\small\implies{\sf }$ 9y = 9x + 27

$\small\implies{\sf }$ 9y – 9x = 27

$\small\implies{\sf }$ 9 ( y – x) = 27

$\small\implies{\sf }$ y – x = 27/9 = 3

$\small\implies{\sf }$ y = 3 + x

★ Putting y = 3 + x in equation 1 ★

$\small\implies{\sf }$ x + 3+ x = 7

$\small\implies{\sf }$ 2x = 7 – 3

$\small\implies{\sf }$ 2x = 4

$\small\implies{\sf }$ x = 2

Therefore "y" will be

$\small\implies{\sf }$ y = 2 + 3 = 5

Hence, The two digit number is 25

Answer 2

The Answer:-

25

Step-by-step explanation:

Given:

Sum of digits of two digit number is 7

After reversing digits the number is reduced by 27

To Find:

What is the number?

Solution: Let the tens digit and unit digit of the number be x and y

→ x + y = 7.............(1)

According to question,

→ The two digit number is 10x + y and after reversing it's digit the number becomes 10y +x

⟹ 10y + x = 10x + y + 27

⟹ 10y – y = 10x – x + 27

⟹ 9y = 9x + 27

⟹ 9y – 9x = 27

=>9(y-x)=27

⟹ y – x = 27/9 = 3

⟹ y = 3 + x

 Putting y = 3 + x in equation 1,

⟹ x + 3+ x = 7

⟹ 2x = 7 – 3

⟹ 2x = 4

⟹ x = 2

Therefore "y" will be

⟹ y = 2 + 3 = 5

Ans:-- The two digit number is 25