For the liquids their heat current are same the ratio of their sp. , heat is `2 : 3` , For fall in temperature `65^(@)`C to `60^(@) C` may take time 200 sec & 400 sec respectively . Find out their ratio of density of liquid .

Explanation

To find the ratio of the densities of the two liquids, we can follow these steps:

### Step 1: Understand the given data
We have two liquids with the following properties:
- The ratio of their specific heats \( S_1 : S_2 = 2 : 3 \)
- The time taken for the temperature to fall from \( 65^\circ C \) to \( 60^\circ C \) is \( 200 \) seconds for the first liquid and \( 400 \) seconds for the second liquid.

### Step 2: Set up the heat current equation
...