Let the fixed monthly salary be
𝑆
S and the commission rate be
𝑟
%
r%.

For the first four months:

Total sales: ₹26,272
Total remuneration: ₹5,284
The commission earned during this period is:

Commission
=
𝑟
100
×
26272
Commission=
100
r
​
×26272
Thus, for the first four months, the total remuneration can be expressed as:

4
𝑆
+
𝑟
100
×
26272
=
5284
(
1
)
4S+
100
r
​
×26272=5284(1)
For the remaining eight months:

Total sales: ₹43,008
Total remuneration: ₹9,376
The commission earned during this period is:

Commission
=
𝑟
100
×
43008
Commission=
100
r
​
×43008
Thus, for the remaining eight months, the total remuneration can be expressed as:

8
𝑆
+
𝑟
100
×
43008
=
9376
(
2
)
8S+
100
r
​
×43008=9376(2)
Solving the Equations:
From equation (1):
4
𝑆
+
𝑟
×
26272
100
=
5284
4S+
100
r×26272
​
=5284
Rearranging gives:

𝑟
×
26272
100
=
5284
−
4
𝑆
100
r×26272
​
=5284−4S
𝑟
=
100
(
5284
−
4
𝑆
)
26272
(
3
)
r=
26272
100(5284−4S)
​
(3)
From equation (2):
8
𝑆
+
𝑟
×
43008
100
=
9376
8S+
100
r×43008
​
=9376
Rearranging gives:

𝑟
×
43008
100
=
9376
−
8
𝑆
100
r×43008
​
=9376−8S
𝑟
=
100
(
9376
−
8
𝑆
)
43008
(
4
)
r=
43008
100(9376−8S)
​
(4)
Equating equations (3) and (4):
100
(
5284
−
4
𝑆
)
26272
=
100
(
9376
−
8
𝑆
)
43008
26272
100(5284−4S)
​
=
43008
100(9376−8S)
​

Cross-multiplying and simplifying gives:

43008
(
5284
−
4
𝑆
)
=
26272
(
9376
−
8
𝑆
)
43008(5284−4S)=26272(9376−8S)
Expanding both sides:

227067072
−
172032
𝑆
=
246553984
−
210176
𝑆
227067072−172032S=246553984−210176S
Combining like terms:

210176
𝑆
−
172032
𝑆
=
246553984
−
227067072
210176S−172032S=246553984−227067072
38144
𝑆
=
19486832
38144S=19486832
𝑆
=
19486832
38144
=
511.13
≈
511
S=
38144
19486832
​
=511.13≈511
Finding
𝑟
r:
Substituting
𝑆
S back into equation (3):

𝑟
=
100
(
5284
−
4
×
511
)
26272
r=
26272
100(5284−4×511)
​

=
100
(
5284
−
2044
)
26272
=
100
(
3240
)
26272
≈
12.3
%
=
26272
100(5284−2044)
​
=
26272
100(3240)
​
≈12.3%
Conclusion:
Fixed monthly salary
𝑆
S = ₹511
Commission rate
𝑟
r ≈ 12.3%