Question

Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. In which year did his income reach Rs 7000?​

Answer 1

$\large\bold{\underline{\underline{Answer:-}}}$

Subba started work in 1995 at annual salary of Rs 5000 & recieved an increment of Rs 200 each year.

We've to find out in which year his income reach at Rs 7000.

⠀⠀${\underline{\sf{\bigstar\: According \ to \ Question \: Now :}}}$

Salary in 1996 [5000 + 200] = 5200

Salary in 1997 [5200 + 200] = 5400

Salary in 1998 [5400 + 200] = 5600

5200, 5400, 5600... so on.

$\star\:\boxed{\textsf{This is in Arithmetic Progression}}$

For any Arithmetic Progression ( AP ), the nth term Formula is Given by :

$\star\: \boxed{\sf{\pink{a_{n} = a + (n - 1)d}}}$

$\bf{Here}\begin{cases}\sf{ \: a_{n} = 7000}\\\sf{\: First \ term \ (a) = 5000}\\\sf{ \: Common \ difference \ (d) = 200}\end{cases}$

$\underline{\bf{\dag} \:\mathfrak{Substituting \ Values \ in \ the \ formula \ :}}$

$:\implies\sf 7000 = 5000 + (n - 1) 200 \\\\\\:\implies\sf 7000 - 5000 = (n -1) 200 \\\\\\:\implies\sf 2000 = (n - 1) 200\\\\\\:\implies\sf n - 1 = \cancel\dfrac{2000}{200}\\\\\\:\implies\sf n - 1 = 10 \\\\\\:\implies\sf n = 10 + 1\\\\\\:\implies\boxed{\frak{\purple{n = 11}}}$

$\therefore\underline{\textsf{ Hence, in 11th years subba's salary will reach at \textbf{Rs \: 7000}}}.$⠀⠀⠀⠀

Answer 2

Answer:

the annual salary received by subban raa in the year 1995,1996,1997....is 5000,5200,5400,...7000

the incomes that subban raa obtained in various year are in A.p as every year his salary is increased by rs 200.

there fore,the salaries of each year after 1995 are 5000,5200,5400

Given

9=5000

d =200

let after 9th year, his salary be rs 7000 an =at ch ÷( )d

7000=5000+(n-1) 200

200 (n-1)=2000

(n-1) =2000

(n-1)=10

(n=11)

Thus in 11th year his salary will be rs 7000

Explanation:

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