Math, asked by User52765795, 7 hours ago

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

Answers

Answered by itzgeniusgirl
92

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.

Answered by Sauron
26

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.

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