Correct Answer - Option 4 : 11
During the 1st minute, only tap 1 would be opened, so 1 litre will be filled by it.
During the 2nd minute, taps 1 and 2 would be opened, so the taps 1 and 2 will fill 1 litre and 2 litres, respectively.
∴ (1 + 2) litres will be filled.
Proceeding in this manner, during the nth minute, n(n+1)/2 litre would be filled.
Now adding ∑n from 1 onwards to N –
⇒ 1 + (1 + 2) + (1+ 2 + 3) + ……… + (1 + 2 + 3 + 4 + …..N) = 286
Or, ∑n(n + 1)/2 = [N(N+1)(N +2)]/6
∴ [N(N + 1)(N +2)]/6 = 286
Now, from options –
Option (1):
If N = 10
[10 × 11 × 12]/6 = 220 ≠ 286
Option (2):
If N = 12
[12 × 13 × 14]/6 = 364 ≠ 286
Option (3):
If N = 9
[9 × 10 × 11]/6 = 165 ≠ 286
Option (4):
If N = 11
[11 × 12 × 13]/6 = 286