The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9.
What is the number?
Answers
Answer:
Let the first digit be
a
Let the second digit be
b
The first condition
a
+
b
=
7
...............................(1)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The second condition
The first order value:
×
×
a
is a counting in tens. So actual value is
10
×
a
×
×
b
is counting in units. So actual value is
1
×
b
The first Order Value
=
10
a
+
b
...............................(2)
'-----------------------------------------------------------------------'
The second order value:
×
×
b
is a counting in tens. So actual value is
10
×
b
×
×
a
is counting in units. So actual value is
1
×
a
The second Order Value
=
10
b
+
a
.........................(3)
'----------------------------------------------------------------------'
From the question
Equation (3)
−
Equation (2)
=
9
.................................(4)
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Putting it all together
Equation 4 becomes
→
(
10
b
+
a
)
−
(
10
a
+
b
)
=
9
9
b
−
9
a
=
9
.
.
...
...
...
...
...
...
...
...
...
...
...
...
...
...
.
.
(
4
a
)
a
+
b
=
7
.
.
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
.
(
1
)
From equation (1)
a
=
7
−
b
Substitute in
(
4
a
)
giving:
9
b
−
9
(
7
−
b
)
=
9
9
b
+
9
b
−
63
=
9
18
b
=
72
b
=
72
18
=
4
Substitute in Equation (1) giving
a
+
b
=
7
→
a
+
4
=
7
a
=
3
Step-by-step explanation:
Let the first digit be
a
Let the second digit be
b
The first condition
a
+
b
=
7
...............................(1)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The second condition
The first order value:
×
×
a
is a counting in tens. So actual value is
10
×
a
×
×
b
is counting in units. So actual value is
1
×
b
The first Order Value
=
10
a
+
b
...............................(2)
'-----------------------------------------------------------------------'
The second order value:
×
×
b
is a counting in tens. So actual value is
10
×
b
×
×
a
is counting in units. So actual value is
1
×
a
The second Order Value
=
10
b
+
a
.........................(3)
'----------------------------------------------------------------------'
From the question
Equation (3)
−
Equation (2)
=
9
.................................(4)
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Putting it all together
Equation 4 becomes
→
(
10
b
+
a
)
−
(
10
a
+
b
)
=
9
9
b
−
9
a
=
9
.
.
...
...
...
...
...
...
...
...
...
...
...
...
...
...
.
.
(
4
a
)
a
+
b
=
7
.
.
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
.
(
1
)
From equation (1)
a
=
7
−
b
Substitute in
(
4
a
)
giving:
9
b
−
9
(
7
−
b
)
=
9
9
b
+
9
b
−
63
=
9
18
b
=
72
b
=
72
18
=
4
Substitute in Equation (1) giving
a
+
b
=
7
→
a
+
4
=
7
a
=
3
3+4=7
Reversing 34 is 43
34 is increased by 9 I.e 34+9=43
Hope it satisfies you.