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

Explanation

Child's savings day wise are,

We can have at most 190 coins
i.e., `1+2+3+4+5+..` to n term = 190
`rArr (n)/(2)[2xx1+(n-1)1]=190`
`rArr n(n+1)=380 rArr n^(2)+n-380=0`
`rArr (n+20)(n-19)=0`
`rArr n=-20 or n=19`
But number of coins cannot be negative
`:.` n=19 (rejecting n=-20)
So, number of days = 19
Total money she saved `=5+10+15+20+...` upto 19 terms
`=(19)/(2)[2xx5+(19-1)5]`
`=(19)/(2)[100]=(1900)/(2)=950`
`{:("So, number of days = 19"),("and total money she shaved = Rs. 950"):}}`