Question

The sum of the digits of a two digit number is 9. If the digits are reversed, the new number deceased by 45. find the original number​

Answer 1

Let ten's digit be x and unit's be y

∴ original no.=10x+y

∵x+y=9

⇒ x=9−y___(1)

New no. found by reversing the digits =10y+x

(10y+x−9)=4(10x+y)

⇒10y+x−9=40x+4y

⇒39x−6y=−9

⇒13x−2y+3=0

⇒13(9−y)−2y+3=0

⇒117+3−15y=0

⇒y=8

x=9−8=1

∴ The original no. is =10×1+8

=18

Hope this will help you

Answer 2

Given : The sum of the digits of a two digit number is 9 & If the digits are reversed, the new decreased by 45.

To Find : Find the original number ?

____________________________

Solution : Let the 1st (unit) digit be x and 2nd (tens) digit is 9 - x.

$~$

• ${\sf\leadsto{Original~no.~=~10(9~-~x)~+~x}}$

$~$

$\pmb{\sf{\underline{According ~to ~the ~Given~ Question~:}}}$

$~$

$\qquad{\sf:\implies{10(9~-~x)~+~x~+~45~=~10x~+~9 - x}}$

$\qquad{\sf:\implies{90~-~10x~+~x~+~x~+~45~=~9x~+~9}}$

$\qquad{\sf:\implies{90~-~9x~+~45~=~9x~+~9}}$

$\qquad{\sf:\implies{135~-~9x~=~9x~+~9}}$

$\qquad{\sf:\implies{126~=~18x}}$

$\qquad{\sf:\implies{x~=~\cancel\dfrac{126}{18}}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{x~=~7}}}}}}$★

$~$

Therefore,

• Original no. = 10(9 - 7) + 7
• 20 + 7
• 27

$~$

Hence,

$\therefore\underline{\sf{The ~original ~number ~is~\bf{\underline{\pmb{27}}}}}$