Question

A two - digit number is such that the product of its digit is 21. If 36 is added to the number, the digits interchange their places. Find the number

Answer 1

Let the number at ten's place be x and that of unit's place be y.

So The original number:

10x+y

From First condition,

xy=21

y=21/x...............(1)

From Second condition,

10x+y+36=10y+x

10y-y+x-10x=36

9y-9x=36

y-x=4........ (2)

Now Substituting the value of y in (2) we get,

21/x-x=4............(From (1))

21-x²/x=4

21-x²=4x

4x+x²-21=0

x²+4x-21=0

x²+7x-3x-21=0

x(x+7) -3(x+7) =0

(x-3) (x+7) =0

(x-3) =0 OR (x+7) =0

x=3 OR x= -7

If we put x=3 in (1)

y=21/3.............(1)

y=7

If we put x=-7 in (1)

y=21/-7..... (1)

y= -3

So the original number:

10x+y

If we put x=3 and y=7 then the original no.

10x+y=10(3) +7=30+7=37

If we put x= -7 and y= -3 then the original no.

10x+y=10(-7) +(-3) =-70-3=-73