Question

A two digit no is such that the product of its digit is 12.when 36 is added to the no the digits are reversed.find the no.

Answer 1

Took 1 day to solve this finally got the answer that i 26 Explanation:
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