and the annual increment be Rs. y
A man starts his job with a certain monthly salary and a fixed increment every year.
If his salary will be Rs. 11000 after 2 years and Rs. 14000 after 4 years of his service.
What is his starting salary and what is the annual increment.
(Q)
Sol.
Let the starting salary be Rs. x
Starting salary
Rs. 100
Annual Increment
Rs. 10
Salary after 1 year =
100
+
10
Salary after 2 years =
100
+
10
Salary after 3 years =
100
+
10
Salary after 4 year =
100
+
10
2 ×
3 ×
4 ×
As per the 1st given condition,
x
+
2
y
= 11000
As per the 2nd given condition,
x
+
4
= 14000
y
........(ii)
.......(i)
Starting salary + 2 (Increment)
Starting salary + 4 (Increment)
In all these examples we can see that
The starting salary and annual increment remains the same
But the no. of year changes
x + y
x + 2y
x + 3y
x + 4 y
x + 2 y
x + 4 y
Since we don’t know the starting salary and annual increment
Let us assume
Salary after 1 year =
Salary after 2 years =
Salary after 4 years =
Salary after 3 years =
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
Starting salary + 3 (Increment)
Starting salary + Increment
What we need to find?
In this sum we have considered starting salary to be ‘x’ and annual increment to ‘y’
A man starts his job with a certain monthly salary and a fixed increment every year.
If his salary will be Rs. 11000 after 2 years and Rs. 14000 after 4 years of his service.
What is his starting salary and what is the annual increment.
(Q)
Subtracting (ii) from (i),
x + 2y = 11000
x + 4y = 14000
–2y
(–) (–) (–)
∴ y = 1500
Substituting y = 1500 in (i),
x
+
= 11000
∴
x
= 11000
∴
x
=
∴
x
= 8000
The starting salary of man is Rs.8000 and his fixed annual increment is Rs.1500.
∴
2 (1500)
+
3000
11000
–
3000
=
– 3000
and the annual increment be Rs. y
Sol.
Let the starting salary be Rs. x
As per the 1st given condition,
+
2
y
= 11000
As per the 2nd given condition,
x
+
4
= 14000
y
........(ii)
.......(i)
x