Raj always saves 50% of his salary. If his salary decreases by 10% , his savings will decrease by $300. How much is Raj's original salary?

Step 1: Let's denote Raj's original salary as X. Since Raj saves 50% of his salary, his savings are 0.5X.

Step 2: If his salary decreases by 10%, his new salary becomes 0.9X. Since his savings decrease by $300, his new savings are 0.5X -$300.

Step 3: However, since he still saves 50% of his new salary, his new savings are also 0.5 * 0.9X = 0.45X.

Step 4: Now we can set up the equation 0.5X - $300 = 0.45X.

Step 5: If we simplify this equation, we get 0.05X = $300.

Step 6: Solving for X, we find that X = $300 / 0.05 =$6000.

So, Raj's original salary is $6000.

To solve this problem, we need to set up a few equations based on the information given.

1. We know that Raj saves 50% of his salary. We can represent his salary as S and his savings as 0.5S.

2. We're told that if his salary decreases by 10%, his savings decrease by $300. We can represent this new salary as 0.9S and his new savings as 0.5S - 300.

3. Since his savings are 50% of his salary, we can set up the equation 0.5(0.9S) = 0.5S - 300.

4. Solving this equation for S will give us Raj's original salary.

Let's solve it:

0.45S = 0.5S - 300 Subtract 0.45S from both sides: 0.05S = 300 Divide both sides by 0.05: S = 300 / 0.05 S = $6000

So, Raj's original salary is $6000.