Question 13. a two-digit number is such that the product of the digits is 8. when 18 is added to the number, then the digits are reversed. the number is:a. 18b. 24c. 42d. 81
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Let the digits as x and y
Acc. To question :
x.y=8_____(I)
Original no.10x.y
Acc to question
10x+y+18=10y+x
10x-x+y-10y=-18
9(x-y)=-18
x-y=-2 _______(2)
Now from eq 1 we have x=8/y
Now putting this in eqn 2 we get y^2-2y-8=0
Now by splitting middle term we have (y-4)(y+2)=0
As the digit cannot be negative therefore y=4 and x= 8/y I.e 8/4=2
Therefore original no. Will be 10x +y=10 x 2 + 4=24
Reversed no. 10y +x = 10 x 4 + 2= 42.
Therefore no. Can be 24 or 42
Acc. To question :
x.y=8_____(I)
Original no.10x.y
Acc to question
10x+y+18=10y+x
10x-x+y-10y=-18
9(x-y)=-18
x-y=-2 _______(2)
Now from eq 1 we have x=8/y
Now putting this in eqn 2 we get y^2-2y-8=0
Now by splitting middle term we have (y-4)(y+2)=0
As the digit cannot be negative therefore y=4 and x= 8/y I.e 8/4=2
Therefore original no. Will be 10x +y=10 x 2 + 4=24
Reversed no. 10y +x = 10 x 4 + 2= 42.
Therefore no. Can be 24 or 42
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