Question

when a two digit number is divided by the sum of its digits the quotient is 4.if the digits are interchanged,the reversed number is 6 less than twice the original number.find the numbers​

Answer 1

Answer:

The number is 24.

Step-by-step explanation:

Let digit at tens place be x and digit at units place be y.

Therefore the no. is (10x+y ).

(10x+y)/(x+y) =4

10x+y=4(x+y)

10x+y=4x+4y

6x=3y

(2x=y )                           ------(1)

When the digits are interchanged.

The new number is  (10y+x)

As the new no is 6 less than twice the original number,

10y+x=2(10x+y)-6

10y+x+6=20x+2y

10y-2y+6=20x-x

8y+6=19x

(8y+6)/19=x

Substitute value of x in equation (1 )

Therefore,

2(8y+6)/19=y

16y+12=19y

12=19y-16y

12=3y

y=12/3=4

y=4

Substituting the value of y in equation (1)

Therefore,

2x=4

x=4/2=2

x=2

y=4

Therefore the no. is

10x+y=10(2)+4=20+4=24

The no. is 24.

Answer 2

Answer:

x = 2

y = 4

Step-by-step explanation:

let the digits be x, y

therefore the number is 10x+y

given,

(10x+y) / (x+y) = 4 ............ ( i )

or, 10x + y = 4x + 4y

or, 10x-4x = 4y-y

or, 3y = 6x

or, y = 2x

10y + x = 2(10 x+ y) -6

or, 10 y + x = 20x + 2 y -6

or, 10y - 2 y + x - 20x = -6

or, 8(2x) -19x = -6

or, 16 x - 19 x = -6

or, -3x = -6

or, x = 2. (ans)

y = 2x

or, y= 2 x 2

or, y = 4. (ans)