Question

subba rao started work in 1995 at an annual salary of5000 and received an increment of Rs 200 each year . in which year did his income reach Rs 7000?

Answer 1

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Answer 2

Step-by-step explanation:

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 :

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

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

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

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

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