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

$<B>Solution:$

Let units place digit be x

then, tens place digit = 15 - x

Number formed :

= 10 ( 15 - x ) + x

= 150 - 10x + x

= 150 - 9x

Reversed number formed :

= 10x + 15 - x

= 9x + 15

It is given that :

9x + 15 = 150 - 9x - 27

=> 9x + 9x = 150 - 27 - 15

=> 18x = 108

=> x = 108/18 = 6

Thus, original number formed:

= 150 - 9 (6)

= 150 - 54

= 96

$<B>[ANSWER: 96]$

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