Solving a Salary Puzzle Using Basic Arithmetic and Proportions

Let's dive into a salary puzzle that utilizes basic arithmetic and proportions to find a solution. The scenario is as follows: Rahul's salary is 50 more than Rohit's salary. If Rahul saves Rs 2250, which is 8% of his salary, then what is Rohit's salary?

Understanding the Problem

To solve this problem, we need to first understand the relationship between Rahul and Rohit's salaries and then use algebraic equations to find the unknown value.

Defining the Variables

We define Rohit's salary as R.

Crafting the Equation for Rahul's Salary

Since Rahul's salary is 50 more than Rohit's salary, we can represent Rahul's salary as:

H R 50

Alternatively, as Rahul's salary is 1.5 times Rohit's salary, we can also express Rahul's salary as:

H 1.5R

Using Savings to Formulate an Equation

The problem states that Rahul saves 8% of his salary, which amounts to Rs 2250. We can represent this as a percentage of Rahul's salary:

0.08H 2250

Substituting Rahul's Salary Expression

Since we know that H 1.5R, we can substitute this into our savings equation:

0.08 * 1.5R 2250

Solving the Equation

Let's simplify this step-by-step:

0.12R 2250

To find Rohit's salary, we divide both sides by 0.12:

R 2250 / 0.12

R 18750

Hence, Rohit's salary is Rs 18750.

Problem-Solving Steps Summary

Define the variables: Rohit's salary as R. Express Rahul's salary as H R 50 or H 1.5R. Use the given savings information: 8% of Rahul's salary 2250. Formulate the equation: 0.08 * 1.5R 2250. Simplify and solve for R: R 2250 / 0.12 18750.

Conclusion

This problem demonstrates how basic arithmetic and algebraic equations can be used to solve real-life salary puzzles. By understanding the relationships between the given values and using simple mathematical operations, we can find the exact value of an unknown variable. The solution to this problem is Rohit's salary is Rs 18750.