Question

A village has $4000$ literate people in the year $2010$ and this number increases by $400$ per year. How many literate people will be there till the year $2020?$ Find a formula to know the number of literate people after $n$ years?

• A. $7200,200n+3800$
• B. $7800,800n+3100$
• C. $7700,600n+3300$
• D. $7600,400n+3600$

Answer 1

Answer: (D)

$7600,400n+3600$

Since the number of literate people increased by 400 every year then the population of literate people every form an A.P.

No. of people in year 2010 (a)=4000

Increment in population every year(d)=400

No. of year from 2010-2120(n)=10

$t_n=a+(n-1)d$

$t_{10}=4000+(10-1)400$

$t_{10}=4000+3600$

$t_{10}=7600$

$\therefore$ 7600 literate people till year 2020.

$t_n=a+(n-1)d$

$t_n=4000+(n-1)400$

$t_n=4000+400n-400$

$t_n=3600+400n$

$\therefore$ There are (3600+400n) people literate after n years.