Question

The sum of 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:

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.

тнαηк үσυ

@itzshivani