The sum of the digits of a two digit number is 10. If the digits change their place, the new number is 18 less than the original number. What is the original number ?
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iamtanish:
No need i got it
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Suppose the digits are
a
and
b
.
The original number is
10
a
+
b
The reversed number is
a
+
10
b
We are given:
a
+
b
=
10
(
a
+
10
b
)
−
(
10
a
+
b
)
=
54
From the second of these equations we have:
54
=
9
b
−
9
a
=
9
(
b
−
a
)
Hence
b
−
a
=
54
9
=
6
, so
b
=
a
+
6
Substituting this expression for
b
into the first equation we find:
a
+
a
+
6
=
10
Hence
a
=
2
,
b
=
8
and the original number was
28
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