Problem 1 :
A man joined a company as Assistant Manager. The company gave him a starting salary of ₹60,000 and agreed to increase his salary 5% annually. What will be his salary after 5 years?
Solution :
Starting salary = 60,000
Every year 5% of annual salary is increasing.
Second year salary = 60000 + 5% of 60000
= 60000(1 + 5%)
Third year salary = 60000 + 5% of 60000(1 + 5%)
= 60000(1 + 5%)(1 + 5%)
= 60000(1 + 5%)2
By continuing in this way, salary after 5 years is
= 60000(1 + 5%)5
= 60000(105/100)5
= 60000(1.05)5
= 76577
Problem 2 :
Sivamani is attending an interview for a job and the company gave two offers to him.
Offer A: ₹20,000 to start with followed by a guaranteed annual increase of 6% for the first 5 years.
Offer B: ₹22,000 to start with followed by a guaranteed annual increase of 3% for the first 5 years.
What is his salary in the 4th year with respect to the offers A and B?
Solution :
Offer A: ₹20,000 to start with followed by a guaranteed annual increase of 6% for the first 5 years.
a = 20000, r = 0.06 and n = 5
Starting salary = 20,000
Every year 6% of annual salary is increasing.
Starting salary = 20000
Second year salary = 20000 + 6% of 20000
= 20000(1 + 6%)
By continuing in this way, we get
4th year salary = 20000(1 + 6%)3
= 20000(1.06)3
= 22820
Offer B: ₹22,000 to start with followed by a guaranteed annual increase of 3% for the first 5 years.
a = 22000, r = 0.03 and n = 5
Starting salary = 22,000
Every year 3% of annual salary is increasing.
Starting salary = 22000
Second year salary = 22000 + 3% of 22000
= 22000(1 + 3%)
By continuing in this way, we get
4th year salary = 22000(1 + 3%)3
= 22000(1.03)3
= 24040
Problem 3 :
If a, b, c are three consecutive terms of an A.P. and x, y, z are three consecutive terms of a G.P. then prove that xb−c × yc−a × za−b = 1 .
Solution :
Since a, b and c are in A.P,
b - a = c - b = d (common difference)
We need to prove,
xb−c × yc−a × za−b = 1
Let us try to convert the powers in terms of one variable.
2b = c + a - a + a
2b = c - a + 2a
2(b - a) = c - a
2d = c - a
If c - b = d, then b - c = -d
If b - a = d, then a - b = -d
L.H.S
xb−c × yc−a × za−b = x−d × y2d × z−d ---(1)
y = √xz
By applying the value of y in (1)
= x−d × (√xz)2d × z−d
= x−d × (xz)d × z−d
= x−d + d z-d + d
= 1
Hence proved.
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