Math, asked by nishasantosh551, 1 year ago

the sum the sum of the digits of a two-digit number is 10 the number formed by reversing the digitis 18 less than the original number find the original number ​

Answers

Answered by sanchari46
60

Step-by-step explanation:

Let the no be 10x+y

Reversed no is 10y+x

10x+y-18=10y+x

= 9x-9y=18

=x-y=2

Given x+y=10

On solving we get x=6

y=4

Req no = 64

Hope it helps ✌️✌️✌️

Answered by Sauron
75

Answer:

The Original Number is 64.

Step-by-step explanation:

Given :

Sum of digits = 10

Number formed after reversing the digits = 18 less than than the Original Number.

To find :

The original number

Solution :

Let the -

  • Units place be x
  • Tens place be y

\textsf{\underline{\underline{According to the question -}}}

The sum of the digits of a two digit number is 10.

\tt{\leadsto} \: x + y = 10 \\  \\ \tt{\leadsto} \:x = 10 - y \: ......(1)

\rule{300}{1.5}

The number formed by reversing the digits is 18 less than the original number.

\tt{\leadsto} \:10x + y + 18 = 10y + x \\  \\  \tt{\leadsto} \:10x - x + y - 10y = - 18 \\  \\ \tt{\leadsto} \:9x - 9y = - 18 \\  \\\tt{\leadsto} \: 9(x - y) = - 18 \\  \\ \tt{\leadsto} \:x - y =  \dfrac{ - 18}{9}  \\  \\ \tt{\leadsto} \: 10 - y - y = - 2  \: ...\gray{[ From  \: Equation (1)]} \\  \\ \tt{\leadsto} \:- 2y = - 12 \\  \\ \tt{\leadsto} \:y =  \dfrac{ - 12}{ - 2} \\  \\\tt{\leadsto} \:y  = 6

\rule{300}{1.5}

Substitute the value of y in equation (1)

\tt{\leadsto} \:x = 10 - 6 \\  \\ \tt{\leadsto} \:x = 4

\rule{300}{1.5}

\textsf{\underline{\underline{The original number - }}}

\tt{\leadsto} \:10y + x \\  \\ \tt{\leadsto} \:10(6) + 4 \\  \\ \tt{\leadsto} \:60 + 4 \\  \\ \tt{\leadsto} \:64

Original number = 64

\therefore The Original Number is 64.

Similar questions