Question

A child puts one five rupee coin from her saving in the piggy bank on the first day. She increases her saving by one five - rupee coin daily. If the piggy bank can hold 190 coins of five rupees in all, find the number of days she can contribute to putting the five rupees of into it and find the total money she saved.

Answer 1

She puts 190 five rupee coins into the piggy bank,

so savings $=190\times 5=Rs.950$

She put the coin one by one each day, so the number of coins is also an AP that goes like 1,2,3,4 ......

190 is the total number of coins that the piggy bank can hold.)

so $S_n$ is 190 where a = 1 and d = 1

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]190=\frac{n}{2}\left[2\right(1)+(n-1\left)1\right]380=n(2+n-1)380=n(n+1)380=n^2+n{n}^2+n-380=0n^2+20n-19n-380=0n(n+20)-19(n+20)=0(n-19)(n+20)=0\Rightarrow n=-20or+19$

n can't be a negative number.

So, n = 19.

She fills 190 coins in 19 days.