Math, asked by aaditya85l4619, 3 months ago

the sum of the digits of a two digit number is 15 if the number formed by reversing the digit is less than the original number by 27 find the original number​

Answers

Answered by shashi1979bala
0

let tens digit of the original number be x

so original number,

10(x) + (15-x)

reversing digits mean

10(15-x) + x

therefore

[10(x) + (15-x)]-[10(15-x)+x] = 27

10x + 15-x - 150+10x-x = 27

10x + 10x + 15 - 150 -x - x = 27

20x - 135 -2x = 27

18x - 135 = 27

18x = 27 + 135

18x = 162

x = 162/18

x = 9

original number = 10(x) + (15-x)

= 10(9) + (15-9)

= 90+6

= 96

Hope it helps❤

Answered by llTheUnkownStarll
2

Let the unit's place = x

The ten's place = 15

 \bull \:  \sf{Original \:  Number  =10(15−x)+x}

 \:  \:  \:   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:   \:  \sf   =150−10x+x

 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \sf \: =150−9x

By reversing the digits, we get

 \sf {New \: number=10x+(15−x)}

 \:  \: \:  \:  \:  \: \:  \:  \:   \sf=10x+15−x

 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    \:  = \boxed{ \sf 9x−15} \blue\bigstar

According to the question

 \sf \: Original \:  number−New \:  number=27

: \implies \sf \: 150−9x−9x+15=27

: \implies \sf{−18x+165=27}

: \implies \sf{−18x=27−165=(−108)}

 : \implies \sf{x= \frac{−18}{−108}=6}

 \sf \: original  \: number=150−9x

 \:  \: \:  \:  \:  \:  \: \:  \:  \:  \:  \: \:  \:  \sf  = 150−9×6

\:  \: \:  \:  \:  \:  \: \:  \:  \:  \:  \: \:  \: \sf  = 150- 54

\:  \: \:  \:  \:  \:  \: \:  \:  \:  \:  \: \:  \:  = \underline{\boxed{\frak{96}}} \: \pink{ \bigstar}

  • Hence, the original number 96.

Thank you!

@itzshivani

Similar questions