Question

the sum of a number of two
digit and of the number formed by reversing the digit is 110 and the difference of the digits is 6 find the number

Answer 1

Answer:

Step-by-step explanation:

Let x be the ten's digit and y be the one,'s digit.

Thus, value of the number=10x+y

Value of the number after reversing the number=10y+x

A.T.Q.,10x+y+10y+x=110

=> 11x + 11y=110

=>x+y=10

Given, x-y=6

x+y=10

Adding both the equations,we get

x + y +x - y= 10+6

=> 2x=16

=>x=8

Therefore,y=2

Thus the number is 82.

Hope it helps

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

Ten's digit be 10p and unit digit be n

The number=10p + n

After reversing=10n + p

${\boxed{\sf\:{Situation}}}$

10p + n + 10n + p = 110

11p + 11n = 110

11(p + n) = 110

p + n = 10 ....... (1)

${\boxed{\sf\:{According\;to\;the\;Question}}}$

p - n = 6 ...... (2)

${\boxed{\sf\:{From\;Equation\;(1)\;and\;(2)}}}$

p + n + p - n = 10 + 6

2p = 16

p = 8

${\boxed{\sf\:{Substitute\;the\;value\;in\;(1)}}}$

8 + n = 10

n = 10 - 8

n = 2

p = 8

n = 2

${\boxed{\sf\:{Original\;Number}}}$

=10p + n

=10 × 8 + 2

= 80 + 2

= 82