Twelve percent of Kalyan monthly salary is equal to sixteen percent of Nandu monthly salary, and Sarnesh monthly salary is half of Nandu monthly salary; if Sarnesh annual salary is Rs. 1.08 lacs, what is Kalyan monthly salary?

Introduction / Context:
This salary based problem tests simultaneous use of percentage relationships and simple ratios. Three persons, Kalyan, Nandu, and Sarnesh, have salaries linked by given conditions. We are told the annual salary of one person and asked to find the monthly salary of another. This is typical of algebra and percentage problems in aptitude tests and trains students to translate word relations into equations.

Given Data / Assumptions:

• Let Kalyan monthly salary be K.
• Let Nandu monthly salary be N.
• Let Sarnesh monthly salary be S.
• Twelve percent of K equals sixteen percent of N.
• Sarnesh monthly salary is half of Nandu salary, so S = N / 2.
• Sarnesh annual salary is Rs. 1.08 lacs, that is Rs. 108,000 per year.
• We must find the value of K in rupees per month.

Concept / Approach:
The approach is to use the annual salary information of Sarnesh to first determine his monthly salary, and from that find Nandu monthly salary. With N determined, we then use the percentage relation between K and N to solve for K. The key equation for K and N is 12% of K equals 16% of N, which can be written as 0.12 * K = 0.16 * N. Solving this gives K as a multiple of N, which we then evaluate using the value of N from Sarnesh salary relation.

Step-by-Step Solution:
Annual salary of Sarnesh is Rs. 108,000.His monthly salary S is 108,000 divided by 12, so S = 108,000 / 12 = 9,000.We are told S = N / 2, so Nandu monthly salary N = 2 * S = 18,000.Relation between K and N is 12% of K equals 16% of N.Write this as 0.12 * K = 0.16 * N.Rearrange for K: K = (0.16 / 0.12) * N.Compute 0.16 / 0.12 = 4 / 3.So K = (4 / 3) * N = (4 / 3) * 18,000 = 24,000.

Verification / Alternative check:
Verify all conditions with K = 24,000 and N = 18,000. Twelve percent of K is 0.12 * 24,000 = 2,880. Sixteen percent of N is 0.16 * 18,000 = 2,880. The two values match, confirming the relation between Kalyan and Nandu. For Sarnesh, Nandu salary is 18,000, so half of that is 9,000, which is the monthly salary we obtained by dividing his annual salary 108,000 by 12. All relations are satisfied, which confirms that K = 24,000 is correct.

Why Other Options Are Wrong:
15,000, 36,000, and 12,500 do not satisfy the equation 0.12 * K = 0.16 * N when N is 18,000.

For each of these values, either the percentage equality fails or they are not in the correct ratio compared to N salary as determined from Sarnesh income.

Common Pitfalls:
Some students mistakenly use annual salaries directly in the percentage relations without converting them to monthly values, which mixes time units and breaks the logic. Others mis-handle the fraction 0.16 / 0.12 and get 1.2 or another incorrect ratio. It is always good practice to write the fraction in simplest integer form, here 16 / 12 simplifies to 4 / 3, before applying it to the known value of N. Consistent units and careful fraction simplification help avoid such mistakes.

Final Answer:
Kalyan monthly salary is Rs. 24,000.