Math, asked by ashishbhardwaj80, 11 months ago

The sum of the digits of a two digits 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 manasa1010
1

Answer:

heya mate there's your answer

answer is 96

Step-by-step explanation:

answer is 96 because the sum of the digits is 9+6=15

and if we reverse the digits it is 69 which is 27 less than original no.96

96-27=69

So required number is 96

hope it helps you

Thank you

Answered by llTheUnkownStarll
36

 \large \fbox{Required Solution:}

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} \purple\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}}} \: \orange{ \bigstar}

  • Hence, the original number 96.

Thank you!

@itzshivani

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