Let's break down the problem step by step:

Notation:

• Let $S_0$ be Anil's total salary 2 years ago.

• Let $F$ be the fixed (constant) part of his salary (which remains unchanged over time).

• Let $V_0$ be the variable part of his salary 2 years ago.

• His total salary 2 years ago is thus: $S_0 = F + V_0$

• Over the next two years, his variable salary increased:

  • In the first year, by 50%, so the variable salary became $1.5V_0$.
  • In the second year, by 33.33%, so it further became: $1.3333 \times 1.5V_0 = 2V_0$

• At the end of two years, his total salary increased by 30%, meaning his new total salary $S_2$ is: $S_2 = 1.3S_0$

Since the fixed salary remains constant, the new total salary at the end of two years is: $S_2 = F + 2V_0$

Now, equate the two expressions for $S_2$: $F + 2V_0 = 1.3(F + V_0)$

Solve for $F$ and $V_0$:

Expand the right-hand side: $F + 2V_0 = 1.3F + 1.3V_0$ Rearrange the terms: $F - 1.3F = 1.3V_0 - 2V_0$ $-0.3F = -0.7V_0$ Simplify: $F = \frac{7}{3}V_0$

Find the percentage of the fixed salary:

The total salary 2 years ago was $S_0 = F + V_0$. Substituting $F = \frac{7}{3}V_0$: $S_0 = \frac{7}{3}V_0 + V_0 = \frac{10}{3}V_0$

The fixed salary as a percentage of the total salary is: $\text{Percentage of fixed salary} = \frac{F}{S_0} \times 100 = \frac{\frac{7}{3}V_0}{\frac{10}{3}V_0} \times 100 = \frac{7}{10} \times 100 = 70\%$

Thus, 70% of Anil's total salary 2 years ago was his fixed salary.

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What happens to the percentage of the fixed salary after the variable salary increases?
2. How would the outcome change if the variable salary increased by different percentages each year?
3. What if Anil's total salary increased by 40% instead of 30%? How would this affect the fixed salary percentage?
4. How would you approach the problem if both the fixed and variable parts increased annually?
5. If the variable salary was initially 50% of the total, how does that affect the final calculation?

Tip: When dealing with percentage changes over multiple years, it's important to apply them sequentially rather than adding them up directly.