Question

Eight time a 2-digit number is equal to three times the number obtained by reversing the order of its digits. If the difference between the digits is 5 ,find the number

Answer 1

Let the unit digit be x ( larger digit )
and tens digit be y ( smaller digit )

Original number :- 10y + x

Reversed number :- 10x + y

= >

8 ( 10y + x ) = 3 ( 10x + y )

80y + 8x = 30x + 3y

80y - 3y = 30x - 8x

77y = 22x

( dividing both side by 11 )

7y = 2x

7y / 2 = x ..... ( i )


x - y = 5 ...... ( ii )


Putting the value of x in ( ii )

x - y = 5

( 7y / 2 ) - y = 5

( 7y - 2y )/2 = 5

5y = 10

y = 2


Putting value of y in ( ii )

x - y = 5

x - 2 = 5

x = 7

Original number :- 10y + x

10 × 2 + 7

20 + 7

27


The required number is 27

Answer 2

Let the number at units digit be x and that at tens digit be y.
Acc. to the problem,we have-

8(10y+x)=3(10x+y)
80y+8x=30x+3y
77y-22x=0. ........eq.(i)

Also, it is given that-
Difference of the digits is 5, there may be 2 cases , if x>y, then x-y=5, or if y>x, then y-x=5

CASE 1
x-y=5
x=5+y

Putting this value of x in eq.(I), we have-
77y-22(5+y)=0
77y-110-22y=0
55y=110

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

CASE 2
y-x=5
x=y-5


Then
77y-22(y-5)=0
77y-22y+110=0
55y=-110
y=-2