# PROBLEM LINK

**Author and Editorialist:** Soumik Sarkar

**Tester:** Avijit Agarwal

# DIFFICULTY

SIMPLE

# PREREQUISITES

Basic maths

# PROBLEM

There are two buckets of water. The water in the first bucket has volume v_1 and temperature t_1. The water in the second has volume v_2 and temperature t_2. It is given t_1 < t_2 and the problem to find if some water from the 2 buckets can be combined to get at least v_3 volume at temperature t_3 .

# EXPLANATION

First of all, it is impossible to get water at temperature less than t_1 or more than t_2. After this check there can be multiple more-or-less equivalent methods to solve this problem. Author’s solution is as follows.

Mixing v_x volume of water at temperature t_1 with v_y volume of water at temperature t_2 yields water at temperature t_3, where

Manipulating the equation, we get

This is the fixed ratio in which the water from the two buckets must be mixed to get temperature t_3.

To get v_3 volume, the conditions

must hold.

Time complexity is \mathcal{O}(1) per case.

# AUTHOR’S AND TESTER’S SOLUTIONS

Author’s solution can be found here

Tester’s solution can be found here.