Let's break down the problem step by step:

Given Information:

1. The salaries of Nehal and Mohan in April are in the ratio of 3:4.

   • Let Nehal's salary in April be $3x$.
   • Let Mohan's salary in April be $4x$.

2. Nehal's salary increments:

   • Nehal gets three increments during the year, one in each successive quarter:
     • First quarter (April-June): salary remains $3x$.
     • Second quarter (July-September): 20% increment.
     • Third quarter (October-December): 25% increment.
     • Fourth quarter (January-March): 20% increment (this will not affect calculations as we are stopping at December).

3. Mohan's salary increments:

   • Mohan gets two increments every four months:
     • First period (April-July): salary remains $4x$.
     • Second period (August-November): 20% increment.
     • Third period (December-March): 25% increment (only December is considered).

Step 1: Nehal's total salary from April to December

We calculate Nehal's salary over three periods (quarters):

1st Quarter: April-June

• Salary per month = $3x$.
• For three months: Total salary = $3x \times 3 = 9x$.

2nd Quarter: July-September

• Salary increases by 20%, so the new salary is: $3x + 0.2 \times 3x = 3x \times 1.2 = 3.6x$
• For three months: Total salary = $3.6x \times 3 = 10.8x$.

3rd Quarter: October-December

• Salary increases by 25%, so the new salary is: $3.6x + 0.25 \times 3.6x = 3.6x \times 1.25 = 4.5x$
• For three months: Total salary = $4.5x \times 3 = 13.5x$.

Nehal's Total Salary (April-December)

$9x + 10.8x + 13.5x = 33.3x$

Step 2: Mohan's total salary from April to December

We calculate Mohan's salary over three periods (four-month blocks):

1st Period: April-July

• Salary per month = $4x$.
• For four months: Total salary = $4x \times 4 = 16x$.

2nd Period: August-November

• Salary increases by 20%, so the new salary is: $4x + 0.2 \times 4x = 4x \times 1.2 = 4.8x$
• For four months: Total salary = $4.8x \times 4 = 19.2x$.

3rd Period: December

• Salary increases by 25%, so the new salary is: $4.8x + 0.25 \times 4.8x = 4.8x \times 1.25 = 6x$
• For one month: Total salary = $6x$.

Mohan's Total Salary (April-December)

$16x + 19.2x + 6x = 41.2x$

Step 3: Ratio of Mohan's total salary to Nehal's total salary

Now, we calculate the ratio of Mohan's total salary to Nehal's total salary:

$\text{Ratio} = \frac{41.2x}{33.3x} = \frac{41.2}{33.3} \approx 1.237$

Thus, the ratio of the total salary earned by Mohan to Nehal till 31 December is approximately 1.237:1.

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Would you like more details or further clarifications?

Relative Questions:

1. How would the ratio change if the increments for both Nehal and Mohan were different?
2. What if the salary increments for Mohan were given quarterly instead of every four months?
3. How does changing the starting ratio of salaries (e.g., 2:3 instead of 3:4) affect the final ratio?
4. What happens to the total salaries if Mohan receives an additional increment in December?
5. How would extending the period beyond December influence the results?

Tip:

Always ensure that you're clear on the timing of salary increments (monthly, quarterly, etc.) and how it affects cumulative earnings across different periods.