The monthly salaries of Pia and Som are in the ratio 5 : 4. From her monthly salary, Pia gives 25% to her mother, 15% towards her sister tuition fees, and 18% towards repayment of a loan. She spends the remaining amount, which equals Rs 2100. What is the monthly salary of Som?

Introduction / Context:
This question combines the ideas of ratios and percentage allocation of income. We know how Pia and Som compare in terms of salary, and we are told how Pia spends her salary in several percentage categories, leaving a fixed amount. We need to work backwards from the remaining amount to find Pia salary, and then use the salary ratio to obtain Som salary. This is a common style of problem in bank exams and other aptitude tests.

Given Data / Assumptions:

• Ratio of salaries of Pia : Som = 5 : 4.
• Pia gives 25% of her salary to her mother.
• Pia spends 15% on her sister tuition fees.
• Pia spends 18% on repayment of a loan.
• The remaining part of her salary equals Rs 2100.
• We assume all percentages are of Pia gross monthly salary.

Concept / Approach:
Let Pia monthly salary be P. Then we convert each percentage into a fraction of P. The total of all percentage allocations plus the remaining amount must equal P. The remaining fraction of her salary, after the given percentages are deducted, multiplied by P should equal Rs 2100. From this, we can solve for P. Once we know P, we use the given ratio 5 : 4 to compute Som salary as (4 / 5) * P.

Step-by-Step Solution:
Let Pia monthly salary be P. She gives 25% to her mother, which is 0.25 * P. She spends 15% on sister fees, which is 0.15 * P. She spends 18% on a loan, which is 0.18 * P. Total percentage spent on these three heads = 25% + 15% + 18% = 58%. Therefore, remaining percentage of salary = 100% − 58% = 42%. So remaining amount = 0.42 * P. Given that this remaining amount is Rs 2100, we have 0.42 * P = 2100. Thus P = 2100 / 0.42 = 5000. So Pia salary is Rs 5000 per month. From the ratio 5 : 4, Som salary = (4 / 5) * 5000 = Rs 4000.

Verification / Alternative check:
We can verify by checking the actual distribution of Pia salary. Twenty five percent of 5000 is 1250, fifteen percent is 750 and eighteen percent is 900. The sum of these three is 1250 + 750 + 900 = 2900. The remainder is 5000 − 2900 = 2100, which matches the given condition. This confirms that P = 5000 is correct and therefore Som salary equal to Rs 4000 is also correct based on the 5 : 4 ratio.

Why Other Options Are Wrong:
If Som salary were 3500, then Pia salary would be 4375, and 42% of that is not 2100. Values 4500, 5000 or 3200 for Som do not match the requirement that Pia remainder be exactly Rs 2100 when the ratio 5 : 4 is applied to connect their salaries.

Common Pitfalls:
A frequent mistake is misreading the percentages and adding or subtracting incorrectly. Another common error is to apply the 25%, 15% and 18% directly to the 2100 instead of to Pia full salary. Some students also forget to use the salary ratio at the end to find Som salary and instead report Pia salary as the final answer. Carefully tracking which quantity each percentage is based on and using the ratio only at the final step avoids these issues.

Final Answer:
The monthly salary of Som is Rs 4000.