Math, asked by sumit3456, 1 year 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

Answers

Answered by Swarup1998
7
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Answered by llTheUnkownStarll
3

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

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