There are two water tanks, A and B; A is much smaller than B. While tank A…
2025
There are two water tanks, A and B; A is much smaller than B. While tank A fills at the rate of one litre every hour, tank B fills as 10, 20, 40, 80, 160, ... litres (at the end of the first hour B has 10 litres, at the end of the second hour it has 20 litres, and so on — the volume in B doubles every hour). If tank B is 1/16 full after 17 hours, what is the total duration required to fill it completely?
- A.
4
- B.
21
- C.
22
- D.
24
Attempted by 5 students.
Show answer & explanation
Correct answer: B
When a quantity doubles every fixed time period, it grows as a geometric progression with common ratio 2. Given the fraction of the full quantity reached at some point in time, the number of further periods needed to reach the whole (a fraction of 1) equals the number of times that fraction must be doubled to reach 1.
Applying this to tank B:
At hour 17, tank B holds 1/16 of its capacity.
Since the volume doubles every hour, at hour 18 it holds 2 times 1/16, which is 1/8.
At hour 19 it holds 2 times 1/8, which is 1/4.
At hour 20 it holds 2 times 1/4, which is 1/2.
At hour 21 it holds 2 times 1/2, which is 1, i.e. completely full.
Cross-check: 1/16 equals 2 to the power minus 4. Doubling four times multiplies this by 2 to the power 4, giving 1 (full). Adding these 4 hours to the 17 hours already elapsed gives 17 plus 4, which is 21, confirming the count.
So tank B becomes completely full at hour 21 — a total duration of 21 hours from the start.