A man accepts a position with an initial salary of ₹26000 per month. It is understood that he will receive an automatic increase of ₹250 in the very next month and each month thereafter.
Find this
(i) salary for the 10th month,
(ii) total earnings during the first year
Given: -
An initial salary that will be given = ₹26000
There will be an automatic increase of ₹250 per month from the very next month and thereafter.
Hint: - In the given information the salaries he receives are in A.P.
Let the number of the month is $\mathrm{n}$.
Initial salary $=a=₹ 26000$
Increase in salary $=$ common difference $=d=₹ 250$
i. Salary for the $10^{\text {th }}$ month,
n = 10,
Salary = a + (n - 1)×d
$=26000+(10-1) \times 250$
$=28250$
∴ Salary for the 10th month = ₹28250
ii. Total earnings during the first year = sum off all salaries received per month.
Total earnings $=\frac{n}{2}[2 \times a+(n-1) \times \mathrm{d}]$
Here n = 12
Total earnings $=\frac{12}{2}[2 \times 26000+(12-1) \times 250]$
$=6 \times(42000+2750)$
$=268500$
Total earnings during the first year = ₹268500