Question

To determine the number of trout in a lake, a conservationist catches 166 trout, tags them and throws them back into the lake. Later, 33 trout are caught; 11 of them are tagged. How many trout would the conservationist expect to be in the lake?​

Answer 1

There are 498 trouts in the lake

Answer 2

There are 498 trouts in the lake

Explanation:

Given:

Number of trouts catch by the conservationist to tag =166

Number of trouts catch later=33

Number of trouts with tags among 33 trouts = 11

To find:

Total number of trouts in the lake=?

Solution:

According to proportionality,

`\frac{\text{Original number of trout caught}}{\text{ total number trouts}} = \frac{\text{number of trouts with tag from the caught tag}}{\text{total number of trouts caught}}`

Substituting the values,

`(166)/(x)=(33)/(11)`

Now applying the cross product principle,

`166 * 33= 11* x`

`5478= 11* x`

`x=(5478)/(11)`

`x=498`