There are two water tanks A and B, A is much smaller than B. While water fills…
2025
There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160…, in tank B. (At the end of the first hour, B has 10 litres, the second hour it has 20, and so on.) If tank B is 1/32 filled after 11 hours, what is the total duration required to fill it completely?
- A.
5 hours
- B.
15 hours
- C.
17 hours
- D.
16 hours
Attempted by 5 students.
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Correct answer: D
When a quantity doubles every fixed time step, its value at any earlier moment equals 1/2ⁿ of the final (full) value, where n is the number of doubling steps still remaining — so the number of hours left equals the number of times that fraction must be doubled to reach 1.
Tank B's contents double every hour (10, 20, 40, 80, 160, …), so the fraction of the tank filled also doubles every hour.
At hour 11, the tank is 1/32 = 1/25 filled.
Doubling once more (hour 12) gives 1/16 = 1/24 filled.
Doubling again (hour 13) gives 1/8 = 1/23 filled.
Doubling again (hour 14) gives 1/4 = 1/22 filled.
Doubling again (hour 15) gives 1/2 = 1/21 filled.
Doubling a fifth time (hour 16) gives the full tank, 1/20 = 1.
So 5 more doublings are needed after hour 11: 11 + 5 = 16 hours in total.
Independently: going from 1/32 filled to completely full means the filled fraction must be multiplied by 32 = 25 — exactly 5 doubling steps, confirming 16 hours as the total duration. Tank A's rate of one litre per hour is irrelevant here, since it only fills tank A, not tank B.