Question

The sum of the digits of a two-digit number is 15. If the number formed by
reversing the digits is less than the original number by 27, find the original
number

Linear Equations In One Variable

Answer 1

solution:-

let the units place be - X

and let the ten's place be - 15 - X

therefore original number = 10 (15 - X) + X = 150 - 10x + X = 150 - 9x

now, by reversing the digits, we get

new number = 10x + (15 - X) = 10x + 15 = 9x - 15

according to the question

original number - new number = 27

⇢ 150 - 9x - 9x + 15 = 27

⇢ -18x + 165 = 27

⇢ -18x = 27 - 165 = -108

$⇢ \: x \: = \frac{ - 108}{ - 18} = 6$

hence original number

⇢ 150 - 9x = 150 - 9 × 6

⇢ 150 - 54

⇢ 96

therefore our required answer is 96.

Answer 2

Answer:

The original number of 96.

Step-by-step explanation:

Let,

• Units digit = x
• Tens digit = 15 - x

Original number :

$\longrightarrow$ 10(15 - x) + x

$\longrightarrow$ 150 - 10x + x

$\longrightarrow$ 150 - 9x

__________________

Number with reversed digits :

• Units place = (15 - x)
• Tens place = x

$\longrightarrow$ 10(x) + (15 - x)

$\longrightarrow$ 10x + 15 - x

$\longrightarrow$ 9x + 15

__________________

If the number formed by reversing the digits is less than the original number by 27,

Original number = Number with reversed digits + 27

$\longrightarrow$ 150 - 9x = 9x + 15 + 27

$\longrightarrow$ -9x - 9x = 42 - 150

$\longrightarrow$ -18x = -108

$\longrightarrow$ x = 108/18

$\longrightarrow$ x = 6

__________________

★ Original number :

$\longrightarrow$ 150 - 9x

$\longrightarrow$ 150 - 9(6)

$\longrightarrow$ 150 - 54

$\longrightarrow$ 96

Original number = 96

Therefore, the original number of 96.