Question

the sum of the digit of a two digit number is 5. If the number is 9 more than the number obtained by interchanging the digits. Find the number. ​

Answer 1

Answer:

23

Step-by-step explanation:

Let xy be the number.

x+y=5

x*10+y+9=10*y+x

that is 9x-9y=-9

or x-y=-1

x+y=5

Adding above two equations

2x=4 ie. x=2

and y=5-x =5-2=3

Therefore number is 23

Adding 9 to 23 gives 32.

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• The sum of two digits = 5
• If the number is 9 more than the number obtained by interchanging the digits

${\bf{\blue{\underline{To\:Find:}}}}$

• Number =?

${\bf{\blue{\underline{Now:}}}}$

• Let the ones place digit be = x
• and 2nd place digit be = y

That's

$: \implies \boxed{\sf{x +y = 5 ....(1) }}$

By interchanging,

• 10x + y + 9 = 10y + x
• 10x - x = 10y -y -9
• 9x - 9y = -9

$: \implies \boxed{\sf{x -y = -1....(2) }}$

________________________________________

From (1),

$: \implies{\sf{x = 5 - y ....(3) }}$

Put value of x in eq (2),

$: \implies{\sf{ 5 - y - y = -1}}$

$: \implies{\sf{ 5 - 2y = -1}}$

$: \implies{\sf{ - 2y= -1-5}}$

$: \implies{\sf{ - 2y= -6}}$

$: \implies{\sf{ y= \frac{ - 6}{ - 2} }}$

$: \implies \boxed{\sf{ y= 3 }}$

_________________________________________

Now put the value of y in eq (3),

$: \implies {\sf{ x = 5 - 3 }}$

$: \implies \boxed{\sf{ x= 2}}$

Therefore the two digit number is 32.