Question

it takes 20days for a pond to get filled with rain water. if the level of water doubles each day, then how long would it take to fill half the pond?

Answer 1

it takes 10 days to fill half the pond

Answer 2

Answer:

On 19th day

Step-by-step explanation:

Given : It takes 20 days for a pond to get filled with rain water. If the level of water doubles each day.

To find : How long would it take to fill half the pond?

Solution :

Let the rate at which pond fills each day be x.

Water level doubles each day, hence  

DAY LEVEL

1  x

2 2x

3 4x

4 8x

5 16x

Water level rises in a series which is geometric series with first term a=x and common ration r = 2

Also, it takes 20 days to fill the pond to its capacity.

According to series, the LEVEL of water in 20 days will be 20th term of the series.

$a_{20} = x\times 2^{20-1}$

$a_{20} = x\times 2^{19}$

Hence capacity of pond is = $x\times 2^{19}$

1/2 of that capacity = $\frac{1}{2}\times x\times 2^{19}$

1/2 of that capacity = $x\times 2^{18}$

Like on day 4, level is  $\Rightarrow x\times 2^{4-1}=8x$

on day 5, level is $\Rightarrow x\times 2^{5-1}=16x$

.....

On day 19, LEVEL will be $\Rightarrow x\times 2^{19-1}=x\times 2^{18}$

Hence on 19th day pond will be 1/2 full.