Question

Sum of the digits of a number of two digits is 8. When we interchange the digits, we see that the difference between the numbers is 18. Find the original number. ​

Answer 1

Let the two numbers are XandY

As per question,

The sum of two digit =8

X+Y=8. ____ (i)

By interchanging that two digit ,we saw that the difference between the two numbers=18

Y-X=18. _____(ii)

By adding two equation,

X+Y=8

+.

Y-X=18

_________

2Y= 26 (+X,-XCancelled)

Y=26/2=13

By putting the value of Y in equation _(i)

X+Y=18

X+13=18

X=18-13

=5

.

. .The two numbers are 13 and 5(Ans)

Answer 2

Answer:

Original Number is 53.

Step-by-step explanation:

Gívєn -

Sum of the Digits of the Number = 8

Difference between the Original Number and Number with Reversed Digits = 18

Tσ fínd -

The Original Number

Sσlutíσn -

Let the -

• Units Place be as x
• Tens place be as 10(8 - x)

$\bf{\implies} \: 80 - 10x + x$

$\sf{\implies} \:\pink{80 - 9x} \: .... [Original \: Number]$

$\rule{300}{1.5}$

✯ Number with Reversed Digits :

Let the -

• Units Place be (8 - x)
• Tens Place be 10(x)

$\bf{\implies} \:10(x) + (8 - x)$

$\sf{\implies} \: 10x + 8 - x$

$\sf{\implies} \:{\pink {9x + 8}} \: .....[Reversed \: Digits]$

$\rule{300}{1.5}$

✯ According to the Question -

Difference between the Original Number and Number with Reversed Digits = 18

$\bf{\implies} \: 80 - 9x - (9x + 8) = 18 \\ \ \sf{\implies} \: 80 - 9x - 9x - 8 = 18 \\\ \sf{\implies} \: 72 - 18x = 18 \\\ \sf{\implies} \: -18x = 18 - 72 \\\ \sf{\implies} \: 18x = 54 \\\ \sf{\implies} \: x = \frac{54}{18} \\\ \sf{\implies} \:x = 3$

$\rule{300}{1.5}$

✯ Original Number =

$\sf{\implies} \: 80 - 9x \\ \sf{\implies} \:80 - 9(3) \\ \sf{\implies} \:53$

Original Number = 53.

$\therefore$ The Original Number is 53