Question

the sum of the digit 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

Answer 1

Let the number with two digits be 10x + y.
Sum of the digits is 15.
⇒ x + y = 15 ----------------- (1)
Number formed by reversing the digits = (10y + x)

(10x + y) - (10y + x) = 27
⇒ 9x - 9y = 27
⇒ x - y = 3 ----------------- (2)
Solving equations (1) and (2), we get x = 9 and y = 6.

Therefore, the original number is 10(9) + 6 = 96.

Answer 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