The monthly salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs 4000 and the new ratio becomes 40 : 57, what is the present salary of Sumit in rupees?

Introduction / Context:
This question checks understanding of ratios combined with linear equations. Salaries that increase by a fixed amount but still keep a new ratio are a standard pattern in aptitude tests and help to build algebraic thinking about proportional relationships.

Given Data / Assumptions:

• Let the original salaries of Ravi and Sumit be in the ratio 2 : 3.
• Each salary is increased by Rs 4000.
• The new ratio of their salaries becomes 40 : 57.
• We have to find the present salary of Sumit in rupees.

Concept / Approach:
If two quantities are in the ratio m : n, we can represent them as m*k and n*k for some common factor k. When the same fixed increment is added to both, a new ratio is formed. We can use this information to form an equation in k and then solve for the actual values. This is a typical application of ratio and proportion with algebra.

Step-by-Step Solution:
Step 1: Let the original salaries be 2x for Ravi and 3x for Sumit. Step 2: After an increase of Rs 4000 each, the new salaries are 2x + 4000 and 3x + 4000. Step 3: We are told that (2x + 4000) : (3x + 4000) = 40 : 57. Step 4: Form the equation (2x + 4000) / (3x + 4000) = 40 / 57. Step 5: Cross multiply: 57(2x + 4000) = 40(3x + 4000). Step 6: Expand: 114x + 2,28,000 = 120x + 1,60,000. Step 7: Rearrange: 2,28,000 - 1,60,000 = 120x - 114x, so 68,000 = 6x. Step 8: Therefore x = 68,000 / 6 = 34,000 / 3. Step 9: Sumit salary = 3x = 3 * (34,000 / 3) = 34,000.

Verification / Alternative check:
Original salaries are 2x = 22,666.67 and 3x = 34,000 approximately. After adding Rs 4000, Ravi salary is about 26,666.67 and Sumit salary is 38,000.67 but in exact algebraic form they fit the 40 : 57 ratio perfectly. Computing 2x + 4000 and 3x + 4000 with x = 34,000 / 3 confirms that their ratio simplifies to 40 : 57, which validates our result.

Why Other Options Are Wrong:
Values like 38,000, 46,800, 50,000 and 36,700 do not satisfy the new ratio when you solve backward to get Ravi salary and then check the 40 : 57 proportion after adding Rs 4000. Only 34,000 is consistent with both the original ratio and the new ratio information.

Common Pitfalls:
Many learners wrongly treat the ratio 2 : 3 as a fixed difference 1x instead of a multiplicative relation. Another frequent error is to form the equation as (2x + 4000) : (3x + 4000) = 2 : 3, which ignores the new ratio given in the statement. Forgetting to cross multiply carefully or making arithmetic mistakes in subtraction of large numbers can also lead to wrong answers.

Final Answer:
The present salary of Sumit is Rs 34,000.