# A vessel of capacity 286 litres, has ŌĆ£nŌĆØ taps, numbered from 1 to N fitted to it. At the start of the nth minute, where, 1Ōēż n Ōēż N, the tap numbered n,

1.1k views
in Aptitude
closed
A vessel of capacity 286 litres, has ŌĆ£nŌĆØ taps, numbered from 1 to N fitted to it. At the start of the nth minute, where, 1Ōēż n Ōēż N, the tap numbered n, which fills the tank at the rate of n litres per minute, is opened. If it takes exactly N minutes to fill the tank in this manner, then, what is the value of N?
1. 10
2. 12
3. 9
4. 11

by (53.1k points)
selected

Correct Answer - Option 4 : 11

During the 1st minute, only tap 1 would be opened, so 1 litre┬Āwill 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.

Ōł┤ (1 + 2) litres will be filled.

Proceeding in this manner, during the nth minute, n(n+1)/2 litre┬Āwould be filled.

Now adding Ōłæn from 1 onwards to N ŌĆō

ŌćÆ 1 + (1 + 2) + (1+ 2 + 3) + ŌĆ”ŌĆ”ŌĆ” + (1 + 2 + 3 + 4 + ŌĆ”..N) = 286

Or, Ōłæn(n + 1)/2 = [N(N+1)(N +2)]/6

Ōł┤ [N(N + 1)(N +2)]/6 = 286

Now, from options ŌĆō

Option (1):

If N = 10

[10 ├Ś 11 ├Ś 12]/6 = 220 ŌēĀ 286

Option (2):

If N = 12

[12 ├Ś 13 ├Ś 14]/6 = 364 ŌēĀ 286

Option (3):

If N = 9

[9 ├Ś 10 ├Ś 11]/6 = 165 ŌēĀ 286

Option (4):

If N = 11

[11 ├Ś 12 ├Ś 13]/6 = 286