Question

Sum of the digits of a two digit number is 15. If number formed by reversing digits is less than original number by 27. Find original number

Answer 1

Answer:

Step-by-step explanation:

Let the number at place value one be y and that at place value ten be x. then the number is 10x+y.

According to the question,

x+y=15

x=15-y

Again,

10y+x=10x+y-27

10y-y=10x-x-27

9y=9x-27

9y=9(15-y)-27

9y=135-9y-27

9y+9y=108

y=108/18

y=6

x=15-6=9

therefore,the number is 10x+y=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