Solution:

According to the question, Mass of hot water (m₁) is 300 g

Temperature (T₁) is 50⁰ C

Mass of cold water (m₂) is 600 g

Change in the temperature of cold water (T – T₂) is 15⁰ C

Let the final temperature be T⁰ C

The specific heat capacity of water is c for both the cases.

Expression for heat energy is Q = mc(change in temperature)

Using the above relation, we can write the expression for hot and cold water

Heat lost by hot water = m₁c (T₁ – T)

Heat gained by cold water = m₂c (T – T₂)

We know that when no heat is lost to surroundings, the heat gained is equal to the heat lost

m₁c (T₁ – T) = m₂c (T – T₂)

Putting values, we get => 300 (50 – T) = 600 (15)

T = 6000 / 300

Therefore, final temperature = 20⁰ C

Change in temperature is 15⁰ C

Then, the initial temperature of cold water becomes 20⁰ C – 15⁰ C

= 5⁰ C