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
Answers
Answered by
7
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
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
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Answered by
1
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
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
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