Question

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 first hour, b has 10 litres , second hour it has 20, and so on). if tank b is 1/32 filled after 21 hours, what is the total duration required to fill it completely?

Answer 1

Step 1:

Water gets filled in B like:

10,20,30,40,......

Step 2:

So it’s a G.P. with first term = 10 and common ratio = 2

Step 3:

21st term of series = $ar^{20}$ = 10 x $2^{20}$

This is equal to I / 32 of the tank's full capacity

Step 4:

Hence full capacity of tank = 32 x 10 x $2^{20}$ = 10 x $2^{25}$  which equals 26th term of series