Hi!
Question :
A village is supplied water through pipe lines every third day. The water was first supplied on 1st January. The last was supplied on 31st January. How many time was water supplied in the month of January? 10,000 kl of water was supplied on 1st January. Subsequently, the quota of water supply was increased by 500 litres each time. How much water was supplied during the month of January?
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Verified answer
Question :---- we have to find how much water was supplied during the month of January ?
Given :----
Formula to be used :-------
Solution :-------
it has been said that, first supply was on 1st jan and last supply and after every 3rd day water is coming and last was on 31st jan .
so,
our AP series will be :----- 1 , 4 ,7 ______________ 31 .
First Term , a = 1
common difference , d = 3
Last term (Tn) = 31 .
First we have to Find for how many days the water supply came . ?
putting values in above formula we get,
31 = 1 + (n-1)3
31 = 1 + 3n - 3
33 = 3n
n = 11 days
So water was supplied for Total 11 days...
_______________________________________
Now lets find out capacity of Total water supplied ?
it has been said that on 1st of jan 10000 kilo-litre of water was supplied , and 500 litre increased every time .
1000 litre = 1 kilo-litre
500 litre = 0.5 kilo-litre .
Now, our AP series will be :-----
10000 , 10000.5 , 10001 _______________ upto 11 terms .
so,
our first term , a = 10000
common difference , d = 0.5
Total terms n = 11.
Putting values in above sum formula we get,
So, According to your value in Question Total 110027.5 kilo-litre of water was supplied during the month of January ....
(Hope it helps you)