1.

A two-digit number is such that the product of its digits is 6. When 9 is added to this number; the digits interchange their places. Find the number.

Answer»

Let 2 digit no be XY

X× Y= 6

XY + 9 = YX

10 X + Y + 9= 10 Y + X

9X - 9 Y+ 9=0

X- Y + 1=0

ALSO X× Y = 6

X= 6/Y

put in x- y+1=0

6/y - y +1=0

6 - y.y+ y= 0

-y.y -2y + 3Y +6 =0

-y(y+2) +3(y+2) =0

y= 3,-2

take y=3

x= 6/3 = 2

SO number is 23


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