A man installs a water tank of 275 lit capacity in his house and fills it completely. If he uses 5 lit of water on the first day, 10 lit on the second day, 15 lit on the third day and so on, after how many days he needs to use the pump again to fill the tank?
A man installs a water tank of 275 lit capacity in his house and fills it completely. If he uses 5 lit of water on the first day, 10 lit on the second day, 15 lit on the third day and so on, after how many days he needs to use the pump again to fill the tank? Correct Answer 10 days
Given:
Capacity of the tank = 275 lit
Concept:
The use of the water forms an AP series.
Formula used:
S = n/2 ×
Where, S = sum of the series, a = first term, n = number of terms, d = common difference of the series.
Calculation:
Let us assume it takes n days to empty the tank based on his usage.
His total use of water in n days
= (5 + 10 + 15 + 20 + 25 + …….. n terms) lit
= n/2 lit
= n/2 (5n + 5) lit
= 5n/2 (n + 1) lit
ATQ,
5n/2 (n + 1) = 275
⇒ n (n + 1) = 110
⇒ n2 + n – 110 = 0
⇒ (n - 10) (n + 11) = 0
⇒ n = 10 or -11
∴ n = 10
∴ After 10 days he again needs to fill his tank.
