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

Answer :-

This question is from the chapter arithmetic progression.

The question says that subba's salary increases by Rs. 200 per year and she started at the annual salary of Rs. 5000 and we are asked that in which year the income reaches Rs. 7000.

As we have first income, So a = Rs. 5000 , we are also given that the common difference is of Rs. 200.

Now let us suppose that the salary becomes Rs. 7000 in nth year.

So, now we have -

• $\rm a = 5000$
• $\rm d = 200$
• $\rm n = n$
• $\rm a_n = 7000$

Substituting the value in the formula -

$\sf a_n = a + ( n - 1 )d$

$\sf 7000 = 5000 + ( n -1) 200$

$\sf 7000 - 5000 = (n-1)200$

$\sf (n-1)200 = 2000$

$\sf (n-1) = \frac{2000}{200}$

$\sf n -1 = 10$

$\sf n = 11$

Hence, After 11 years his incomes will be 7000 i.e. in the year 2006 his income will be Rs. 7000

Answer 2

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$\small\sf\underline\pink{Given:-}$

• First term (a) = 5000

• Common difference (d) = 200

• nth term (an) = 7000

$\small\sf\underline\green{To \: Find:-}$

• In which year did his income reach Rs 7000(n) = ?

$\small\sf\underline\orange{Solution:-}$

We know that,

• $\large\boxed{\underline{\blue{\sf a_n=a+(n-1)d}}}$

Here,

$\pink\leadsto\sf{a_n=7000}$

$\pink\leadsto\sf{a=5000}$

$\pink\leadsto\sf{n=?}$

$\pink\leadsto\sf{d=200}$

So,

$:\implies\sf{7000=5000+(n-1)\times200}$

$:\implies\sf{7000-5000=(n-1)\times200}$

$:\implies\sf{2000=(n-1)\times200}$

$:\implies\sf{\dfrac{2000}{200} =(n-1)}$

$:\implies\sf{10 =(n-1)}$

$:\implies\sf{n-1=10}$

$:\implies\sf{n=10+1}$

$\sf:\implies\underline{\boxed{\pink{\mathfrak{n = 11}}}}$

$\displaystyle\therefore\:\underline{\textsf{In\:the\:11th\:year\:Subba\:Rao\:income\:has\:reached\textbf{ Rs.7000}}}$

Finding 11th year :-

• 1st year = 1995

• 2nd year = 1996

• 3rd year = 1997

Now,

• 11th year = 1995 + 11 = 2006.

$\displaystyle\therefore\:\underline{\textsf{In\:2006\:Subba\:Rao\:income\:has\:reached\textbf{ Rs.7000}}}$

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