Question

The sum of the digits 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

Answer:

x = 9, so y = 15–9 = 6, and so the answer is 96. The sum of two digits numbers is 7. If the digits are reversed, the new number is increased by three less than four times the original number

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