A man starts with a certain monthly salary and earns a fixed increment every year. If his salary was Rs. 1500 after 4 years of service and Rs. 1800 after 10 years of service. What was his starting salary?

Question

Accepted Answer

To determine the starting salary of the man, we need to analyze the information given about his salary increments over the years.

1. **Understanding the Problem:**
   - After 4 years of service, his salary is Rs. 1500.
   - After 10 years of service, his salary is Rs. 1800.
   - The salary increases by a fixed amount every year.

2. **Setting Up the Equations:**
   - Let the starting salary be Rs. $ S $.
   - Let the annual increment be Rs. $ I $.

From the information given:
   - After 4 years: $ S + 4I = 1500 $
   - After 10 years: $ S + 10I = 1800 $

3. **Solving the Equations:**
   - We have two equations:
     1. $ S + 4I = 1500 $
     2. $ S + 10I = 1800 $

- Subtract equation 1 from equation 2 to find $ I $:
     $$
     (S + 10I) - (S + 4I) = 1800 - 1500
     $$
     $$
     6I = 300
     $$
     $$
     I = 50
     $$

- Substitute $ I = 50 $ back into equation 1 to find $ S $:
     $$
     S + 4(50) = 1500
     $$
     $$
     S + 200 = 1500
     $$
     $$
     S = 1300
     $$

4. **Conclusion:**
   - The starting salary $ S $ is Rs. 1300, which corresponds to Option 3.

5. **Explanation of Incorrect Options:**
   - **Option 1 (Rs. 1100):** If the starting salary were Rs. 1100, then after 4 years with an increment of Rs. 50 per year, the salary would be $ 1100 + 4 \times 50 = 1300 $, which does not match the given Rs. 1500.
   - **Option 2 (Rs. 1200):** If the starting salary were Rs. 1200, then after 4 years with an increment of Rs. 50 per year, the salary would be $ 1200 + 4 \times 50 = 1400 $, which does not match the given Rs. 1500.
   - **Option 4 (Rs. 1400):** If the starting salary were Rs. 1400, then after 4 years with an increment of Rs. 50 per year, the salary would be $ 1400 + 4 \times 50 = 1600 $, which does not match the given Rs. 1500.

Therefore, the correct starting salary is Rs. 1300, making Option 3 the correct answer.