Question

a two digit is such that the product of the digit is 12 when 36 is added to the number the digits interchange their places find the number

Answer 1

Let the unit's digit in the number be
x
, then as product of digits is
12
, the ten's digit in the number is
12
x
.

Hence, the value of the number is
10
×
12
x
+
x
=
120
x
+
x

On reversing the digits, unit's digit becomes ten's digit and ten's digit becomes unit's digit and its value will become

10
x
+
12
x

It is apparent that
10
x
+
12
x
is greater than
120
x
+
x
by
36

Hence
10
x
+
12
x
=
120
x
+
x
+
36

or
9
x
=
120
−
12
x
+
36

or
9
x
=
108
x
+
36
and dividing each term by
9
we get

x
=
12
x
+
4
and now multiply each by
x
to get

x
2
=
12
+
4
x
or
x
2
−
4
x
−
12
=
0

i.e.
x
2
−
6
x
+
2
x
−
12
=
0

or
x
(
x
−
6
)
+
2
(
x
−
6
)
=
0

i.e.
(
x
+
2
)
(
x
−
6
)
=
0

Hence,
x
=
−
2
or
x
=
6

But we cannot have negative number in units place

Hence,
6
is in unit's place and in ten's place we have
12
6
=
2

and number is
26