Question

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 ​

Answer 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

Answer 2

$\large \fbox{Required Solution:}$

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