Question

A two digit number becomes 5/6 of the reversed number obtained when the digits are interchanged.The difference between the digits is 1.Find the numbers.

Answer 1

let the digit at ten be x
unit be y
original number= 10x+y
interchange number = 10y + x
from 1st condition
$10x + y \times \frac{5}{6} = 10y + x \\ 50x + 5y = 60y + 6x \\ 50x - 6x = 60y - 5y \\ 44x = 55y \\ 4x = 5y \\ 4x - 5y = 0......1$
from 2nd condition
$x - y = 1.....2$
multiply 2 with -4
$- 4x + 4y = - 4....3$
adding 1 and 3 we get
y=4
put y=4 in 2
$x - y = 1 \\ x - (4) = 1 \\ x = 5$
therefore origanal number is 54
and interchange number is 45.
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Answer 2

Step-by-step explanation:

let x = the first digit and (x + 1) the second digit

A two digit number can then be 10x + (x + 1)

[the first digit times ten plus the second digit]

The reverse of that number would then be 10(x + 1) + x

[same reasoning as above but with x and (x + 1) reversed]

The first number becomes or is equal to 5/6 of the reversed number

Equation of this is 10x + (x + 1) = 5/6(10(x + 1) + x)

DISTRIBUTE

10x + (x + 1) = 5/6((10x + 10) + x)

SIMPLIFY

11x + 1 = 5/6(11x + 10)

MULTIPLY both sides by 6 [this leaves NO fractions]

6(11x + 1) = 6(5/6(11x + 10)

66x + 6 = 5(11x + 10)

DISTRIBUTE 66x + 6 = 55x + 50

SUBTRACT 55x and 6 from both sides

66x - 55x + 6 - 6 = 55x - 55x + 50 - 6

11x + 0 = 0 + 44

ADDITION IDENTITY [z + 0 = z]

11x = 44

DIVIDE both sides by 11

11x/11 = 44/11

1x = 4

MULTIPLY IDENTITY [1z = z]

x = 4 therefore x + 1 = 5

The first 2 digit number is 45 and the second is 54 (reverse the digits)

CHECK:

45 = 5/6(54)

MULTIPLY both sides by 6/5 [the reciprocal of 5/6[

6/5(45) = 6/5(5/6)54

54 = 1(54)

MULTIPLY IDENTITY [1z = z]

54 = 54 IT CHECKS

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